LennartNaeve_code/merging_tweezer_code/bosons/2025_03_13 (calc J,U).ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# With a good 3D solution, calculate the values of $J$ and $U_1$, $U_2$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import sympy as sp\n",
    "from scipy import constants as const\n",
    "from scipy import sparse\n",
    "from scipy.integrate import simpson\n",
    "import pickle\n",
    "\n",
    "#add relative path to backend\n",
    "import sys\n",
    "sys.path.append('../../clean_diag/backend')\n",
    "\n",
    "import trap_units as si"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Import solution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "timecode = \"2025-03-19_11-05-43\"\n",
    "\n",
    "data = np.load(f\"data/{timecode}_results.npz\",allow_pickle=True)\n",
    "for key in data.keys():\n",
    "    globals()[key] = data[key]\n",
    "\n",
    "ham = sparse.load_npz(f\"data/{timecode}_hamiltonian.npz\")\n",
    "\n",
    "with open(f\"data/{timecode}_trap.npz\", 'rb') as file:\n",
    "    trap = pickle.load(file)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "omega_r1: 13361.1Hz, omega_r2: 13361.1Hz\n",
      "omega_z1: 1454.4Hz, omega_z2: 1454.4Hz\n"
     ]
    }
   ],
   "source": [
    "omega_z1 = sp.sqrt(4*trap.power_tweezer1*trap.a/sp.pi**3/trap.m) * trap.wvl/trap.waist_tweezer1**3\n",
    "omega_z2 = sp.sqrt(4*trap.power_tweezer2*trap.a/sp.pi**3/trap.m) * trap.wvl/trap.waist_tweezer2**3\n",
    "\n",
    "omega_r1 = sp.sqrt(2*trap.power_tweezer1*trap.a/sp.pi/trap.m) * 2/trap.waist_tweezer1**2\n",
    "omega_r2 = sp.sqrt(2*trap.power_tweezer2*trap.a/sp.pi/trap.m) * 2/trap.waist_tweezer2**2\n",
    "\n",
    "print(f\"omega_r1: {float(trap.subs(omega_r1)):.1f}Hz, omega_r2: {float(trap.subs(omega_r2)):.1f}Hz\")\n",
    "print(f\"omega_z1: {float(trap.subs(omega_z1)):.1f}Hz, omega_z2: {float(trap.subs(omega_z2)):.1f}Hz\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Check how it looks:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ytHv3bo/blJWVKSsry7Ru3LhxKi4uVmNjoyIjIzvluADQGc7c4tEb59mHJk2a5FhfWlqqiRMnetwmIyNDL7zwgmmdp9mHnM2dO1dffPGF/uu//ovZhwAErZycHOXk5Hh8bd26dW7rxowZo3379vm8f0/7AIBgw+B0APCuM34kLkl2u1133HGHfv3rX+vVV1/ViRMnuuJ0AAAWYLAlEMSaZVOzLPqFuEX7AYBAZFVekpUAQlln1JZ1dXWm9dHR0W4zttXW1sput7vNyhYfH+82G9sZNTU1Hts3NTWptrZWCQkJXvvYkeMCgOTf2pLZhwAEC65bAoBv/H3dksHpAIKBv7KyM38kvnDhQvXr10/Tpk3zeltyAPCVv2vL7oLBlkAQ4zbiAOAbpkwHAO86o7Z0nRFt/vz5WrBggcdtbDbzsQ3DcFvnrb2n9d6097gA4M/aktmHAAQLrlsCgG+4bgkA3lmdlb78QFzqvB+J79q1S8XFxXr77bfP4mwAwB21ZddgsCUAAAAAoFNUVVWZbo3r6aJlXFycwsPD3S5QHjt2zO3C5BkDBgzw2D4iIkJ9+/b1qW8dOS4ABAJmHwIAAAAAoOPa8wNxydofiX/xxRe68847tWbNGsXFxbWz5wCAQMBgSyCI8QtxAPANv+IBAO86o7aMjY01Dbb0JCoqSmlpaSotLdWkSZMc60tLSzVx4kSP22RkZOiFF14wrdu+fbvS09Mdt+LxpiPHBQCJ2hIAfMF1SwDwDbUlAHhndVb68gNxqXN+JL5//34dOnRIN954Y0u/mpslSREREXrvvfc0bNiw9p8cAIjasqsw2BIAAAAAnLX2GdLo0l50K3l5eZo6darS09OVkZGh1atXq7KyUtnZ2ZKk/Px8HTlyROvXr5ckZWdna/ny5crLy9OMGTNUVlam4uJibdy40bHPhoYGHThwwPH4yJEjevvtt9WzZ09961vf8um46Cb4t20t1/eT63IAAACBqytr4baORc0IdA/8W+86zu811z3c+PIDcalzfiQ+fPhwvfPOO6bX586dqy+++EL/9V//5TbrJro5chMISAy2BIIYvxAHAN/wKx4A8M6fteWUKVN0/PhxLVy4UNXV1UpNTVVJSYkGDx4sSaqurlZlZaWjfXJyskpKSpSbm6sVK1Zo4MCBWrZsmSZPnuxoc/ToUY0YMcLxvKCgQAUFBRozZox27Njh03EBwBNqSwDwjuuWAOAbaksA8M6fWWn1j8RjYmKUmppqOsZ5550nSW7rAaC9qC27BoMtgSDGRUsA8A2FJQB45+/aMicnRzk5OR5fW7dundu6MWPGaN++fa3ub8iQITIM7z/db+u4AOAJtSUAeOfv2hIAggW1JQB458+s7IwfiQNAZ6G27BoMtgQAAAAAAAAAAAAAAABcWP0jcV/2AQAIXAy2BIKYIalZ1owo9z7nDwAEL6vykqwEEMqoLQHAN9SWAOAdtSUA+IbaEgC8IysBwDfkZddgsCUQxLgdDwD4hinTAcA7aksA8A21JQB4R20JAL6htgQA78hKAPANedk1wvzdAQAAAAAAAAAAAAAAAAAAgEDGzJZAEOMX4gDgG37FAwDeUVsCgG+oLQHAO2pLAPANtSUAeEdWAoBvyMuuwcyW6BqGBQsCTlFRkZKTkxUTE6O0tDS9+uqrbbbfuXOn0tLSFBMTo6FDh2rVqlWm1/fv36/JkydryJAhstlsKiws7MTeAwAAtJPNZQEQvPis2XV4rwEAAOANNSMQuriW5n/8NwCCC/9mgYDHzJZAEPPnL8Q3b96s2bNnq6ioSKNGjdITTzyh8ePH68CBA0pKSnJrX1FRoQkTJmjGjBnasGGDdu3apZycHPXr10+TJ0+WJJ06dUpDhw7Vj3/8Y+Xm5lpyXgAg8SseAPAFsw8BgG+oLQHAO2pLAPANtSUAeEdWAoBvyMuuwWBLIIj586Ll0qVLNW3aNE2fPl2SVFhYqG3btmnlypVavHixW/tVq1YpKSnJMVtlSkqK9u7dq4KCAsdgyyuuuEJXXHGFJGnOnDlncTYAYEZhCQDe8YU4APiG2hIAvKO2BADfUFsCgHdkJQD4hrzsGtxGHEC7NTQ0qLy8XFlZWab1WVlZ2r17t8dtysrK3NqPGzdOe/fuVWNjY6f1FQAAAAAAAAAAAAAAAADOFjNbAkHMMGwyLBpRfmY/dXV1pvXR0dGKjo42rautrZXdbld8fLxpfXx8vGpqajzuv6amxmP7pqYm1dbWKiEh4WxPAQBaZVVeWpW5ABCIOqO2BIBQRG0JAN5RWwKAb6gtAcA7shIAfENedg0GWwJBrFk2Ncui2/H8334SExNN6+fPn68FCxZ43MZmMx/bMAy3dd7ae1oPAFazKi+tylwACESdUVsCQCiitgQA76gtAcA31JYA4B1ZCQC+IS+7BoMtAZhUVVUpNjbW8dx1VktJiouLU3h4uNsslseOHXObvfKMAQMGeGwfERGhvn37WtBzAAAAAAAAAAAAAAAAAOgcDLYEglizYVOzRdP3ntlPbGysabClJ1FRUUpLS1NpaakmTZrkWF9aWqqJEyd63CYjI0MvvPCCad327duVnp6uyMjIs+w9ALTNqry0KnMBIBB1Rm0JAKGI2hIAvKO2BADfUFsCgHdkJQD4hrzsGgy2hHUMP+6ff+ddLi8vT1OnTlV6eroyMjK0evVqVVZWKjs7W5KUn5+vI0eOaP369ZKk7OxsLV++XHl5eZoxY4bKyspUXFysjRs3OvbZ0NCgAwcOOB4fOXJEb7/9tnr27KlvfetbXX+SAAAAbXGuQTu7FgZw9vh36n/O/w34HA90S1Zfq7d1MNsDpR8AAA+oGYHgxr/bwOb634c6FgCAdmOwJRDEDMMmw6Krw+3dz5QpU3T8+HEtXLhQ1dXVSk1NVUlJiQYPHixJqq6uVmVlpaN9cnKySkpKlJubqxUrVmjgwIFatmyZJk+e7Ghz9OhRjRgxwvG8oKBABQUFGjNmjHbs2HF2JwigW7MqL63KXAAIRP6sLQEgmFBbAoB31JYA4BtqSwDwjqwEAN+Ql12DwZZAEPP37XhycnKUk5Pj8bV169a5rRszZoz27dvX6v6GDBkiw+AnVACsx5TpAOCdv2tLAAgW1JYA4B21JQD4htoSALwjKwHAN+Rl1wjzdwcAAAAAAAAAAAAAAAAAAAACGTNbAkGM2/EAgG+YMh0AvKO2BADfUFsCgHfUlgDgG2pLAPCOrAQA35CXXYPBlkAQMyy8HQ9hCSCUWZWXZCWAUEZtCQC+obYEAO+oLQHAN9SWAOAdWQkAviEvuwa3EQcAAAAAAAAAAAAAAAAAAGgDgy2BIGZIMgyLFn+fDAB0Isvy0t8nAgCdiNoSAHxDbQkA3lFbAoBvqC0BwDuyEgB848+8LCoqUnJysmJiYpSWlqZXX321zfY7d+5UWlqaYmJiNHToUK1atcqtzXPPPaeLL75Y0dHRuvjii7VlyxbT64sXL9YVV1yhXr16qX///rrpppv03nvvdaD37cNgS5wdw2mhH12uWTZLFwAIVWQlAHhHbYmQY6jbflYMCkH834esBNpm2FpfTGyG74uPxzrbdh3tk8/n3I1QWwIWsbVj6aounX18+y6Ia0ZfkZXwu7ZypKOvdREjzGmJMFpfwl0Wp+06tU+ux22rj53YJ58F8N8CWYmQ14n/jgIxK23NTovdZlrCmlpfnLeDZ/7Ky82bN2v27Nl68MEH9dZbb2n06NEaP368KisrPbavqKjQhAkTNHr0aL311lt64IEHdN999+m5555ztCkrK9OUKVM0depU/eMf/9DUqVN1yy236PXXX3e02blzp2bOnKk9e/aotLRUTU1NysrK0ldffdWxN9BHEZ26dwAAAAAAAAAAAAAAAAAAEHKWLl2qadOmafr06ZKkwsJCbdu2TStXrtTixYvd2q9atUpJSUkqLCyUJKWkpGjv3r0qKCjQ5MmTHfsYO3as8vPzJUn5+fnauXOnCgsLtXHjRknSiy++aNrvU089pf79+6u8vFzXXHNNZ50uM1sCwcwwbJYuABCqyEoA8I7aEgB8Q1YCgHfUlgDgG7ISALwjKwHAN/7Iy4aGBpWXlysrK8u0PisrS7t37/a4TVlZmVv7cePGae/evWpsbGyzTWv7lKSTJ09Kks4//3yf+98RzGwJAAAAAAAAAAAAAAAAAAAkSXV1dabn0dHRio6ONq2rra2V3W5XfHy8aX18fLxqamo87rempsZj+6amJtXW1iohIaHVNq3t0zAM5eXl6eqrr1ZqaqpP59dRQTOz5eLFi3XFFVeoV69e6t+/v2666Sa99957/u4W4FfNhs3SBaGBvATckZVwRVYC7qgt4Ql5CbgjK+GKrATcUVvCFVkJeEZWwhV5CbgjK+GKrAQ8szovExMT1bt3b8fi6ZbgZ9hs5ow1DMNtnbf2ruvbs8+f//zn+uc//+m4xXhnCprBljt37tTMmTO1Z88elZaWqqmpSVlZWfrqq6/83TXAbwzD2gWhgbwE3JGVcEVWAu6oLeEJeQm4IyvhiqwE3FFbwhVZCXhGVsIVeQm4IyvhiqwEPLM6L6uqqnTy5EnHkp+f73bMuLg4hYeHu804eezYMbeZKc8YMGCAx/YRERHq27dvm2087fMXv/iFtm7dqr/97W+64IILfH6/OipobiP+4osvmp4/9dRT6t+/v8rLy3XNNdf4qVcAEHjISwDwjqwEAN+QlwDgHVkJAN6RlQDgG/ISALwjK4GuERsbq9jY2DbbREVFKS0tTaWlpZo0aZJjfWlpqSZOnOhxm4yMDL3wwgumddu3b1d6eroiIyMdbUpLS5Wbm2tqk5mZ6XhuGIZ+8YtfaMuWLdqxY4eSk5PbfY4dETQzW7o6efKkJOn888/3c08A/zEMm6ULQhN5CVibl53l888/19SpUx3TsE+dOlUnTpzwcl6GFixYoIEDB6pHjx669tprtX///lbbjh8/XjabTf/7v/9r/QkEObISoLaEb8hLIDhqS/gXWQlQW8I7shL4BlkJb8hLgKyEd2Ql8A1/5WVeXp6efPJJrV27VgcPHlRubq4qKyuVnZ0tScrPz9ddd93laJ+dna3Dhw8rLy9PBw8e1Nq1a1VcXKz777/f0WbWrFnavn27HnvsMb377rt67LHH9NJLL2n27NmONjNnztSGDRv0zDPPqFevXqqpqVFNTY2+/vrrs3sjvQiamS2dGYahvLw8XX311UpNTW21XX19verr6x3P6+rquqJ7QJexsiikuAxNvuQlWYnuwKq87MysvP322/XJJ584fo3305/+VFOnTnX7VY+zJUuWaOnSpVq3bp2+/e1v65FHHtHYsWP13nvvqVevXqa2hYWFstnIek+oLYFvUFvCG2pL4BvBUFvCf6gtgW9QW6ItZCXQgtoSbSEvgW+QlWgLWQm08FdeTpkyRcePH9fChQtVXV2t1NRUlZSUaPDgwZKk6upqVVZWOtonJyerpKREubm5WrFihQYOHKhly5Zp8uTJjjaZmZnatGmT5s6dq3nz5mnYsGHavHmzRo4c6WizcuVKSdK1115r6s9TTz2le+65p51n7bugHGz585//XP/85z/12muvtdlu8eLF+vWvf91FvULAMJweUy+hm/MlL8lKwP8OHjyoF198UXv27HEUiGvWrFFGRobee+89XXTRRW7bGIahwsJCPfjgg/rRj34kSfr973+v+Ph4PfPMM/rZz37maPuPf/xDS5cu1ZtvvqmEhISuOakgQm3ZNpvRxott1F1ddt2qjeP63PdO6EenHgvwk06vLdv6LNfR17pIoGelW/98fM/89h1EEP8tAN21tmwzL5xCyAiXx8eSyz9hl9yy2VtW2JpbP7DPueXcJ6d7P7n1ybm2dN2Fc5/svvWpzf9fAN1Id83KNjllhRHmFBZuueSchy7J5JSPptc6mD2mzHLanymHXdq5Hcq5/07n1eE6k3oP3YxlednWZ6dA5/o52jlLopxOJNpuamdzbtfkcrPPBqfnjc755nqwDvQp0mmjKHNg2iJanhuux6p3CsyGDvQpEAXz3x2CSkDXls7/DjqzjgnArHT7/Ou0XVhTy+rwevP+bE6vGS5dao5ueWyPcnohzHwwy69ptvbfESY5OTnKycnx+Nq6devc1o0ZM0b79u1rc58333yzbr755lZfNwz//AcJutuI/+IXv9DWrVv1t7/9TRdccEGbbfPz83Xy5EnHUlVV1UW9BLpGs2GzdEFo8TUvyUp0B1ZnZV1dnWlx/iVcR5SVlal3796mX+JcddVV6t27t3bv3u1xm4qKCtXU1CgrK8uxLjo6WmPGjDFtc+rUKd12221avny5BgwYcFb9DEXUlkALaku0hdoSaEFWojXUlkALaku0hqwEzMhKtIa8BFqQlWgNWQmYkZddI2gGWxqGoZ///Od6/vnn9corryg5OdnrNtHR0YqNjTUtABDq2puXZCXQfomJierdu7djWbx48Vntr6amRv3793db379/f9XU1LS6jSTFx8eb1sfHx5u2yc3NVWZmpiZOnHhWfQw11JYA4BtqSwDwjtoSALwjK4HAVFRUpOTkZMXExCgtLU2vvvpqm+137typtLQ0xcTEaOjQoVq1apXp9TVr1mj06NHq06eP+vTpo+uvv15vvPFGZ55CyCEvAcA7shKAPwXNbcRnzpypZ555Rn/605/Uq1cvxyCC3r17q0ePHn7uHeAfhvHNYtW+EBrIS8CdVXl5Zh9VVVWmD2HR0dEe2y9YsMDrLQnefPNNSZLN5v4LIcMwPK535vq68zZbt27VK6+8orfeeqvNfXRHZCXgjtoSnpCXgDura0sEP7IScEdtCVdkJeCZP2vLzZs3a/bs2SoqKtKoUaP0xBNPaPz48Tpw4ICSkpLc2ldUVGjChAmaMWOGNmzYoF27diknJ0f9+vXT5MmTJUk7duzQbbfdpszMTMXExGjJkiXKysrS/v37NWjQoLM9zW6BvATc8TkcrshKwDPysmsEzcyWK1eu1MmTJ3XttdcqISHBsWzevNnfXQP85pugtFm0+PtsYBXyEnBnXV5+sz/XX761Ntjy5z//uQ4ePNjmkpqaqgEDBujf//632/affvqp28yVZ5y5JbjrzJfHjh1zbPPKK6/oo48+0nnnnaeIiAhFRHzzO5vJkyfr2muv7chbGTLISsAdtSU8IS8Bd1bXlu3F7EOBh6wE3FFbwhVZCXjmz9py6dKlmjZtmqZPn66UlBQVFhYqMTFRK1eu9Nh+1apVSkpKUmFhoVJSUjR9+nT95Cc/UUFBgaPN008/rZycHF1++eUaPny41qxZo+bmZr388ssdfYu6HfIScOfvz+EIPGQl4Bl52TWCZmZLg/+SAOAT8hIIHHFxcYqLi/PaLiMjQydPntQbb7yhK6+8UpL0+uuv6+TJk8rMzPS4TXJysgYMGKDS0lKNGDFCktTQ0KCdO3fqsccekyTNmTNH06dPN2136aWX6ne/+51uvPHGszm1oEdWAoBvyEsgsDD7UGAiKwHAO7ISCCwNDQ0qLy/XnDlzTOuzsrK0e/duj9uUlZUpKyvLtG7cuHEqLi5WY2OjIiMj3bY5deqUGhsbdf7551vX+RBHXgKAd2QlAH8KmpktAbiz7tfh3ywAEKoCPStTUlJ0ww03aMaMGdqzZ4/27NmjGTNm6Ac/+IEuuugiR7vhw4dry5Ytkr65ffjs2bO1aNEibdmyRf/61790zz336JxzztHtt98u6ZvZL1NTU02LJCUlJSk5OblTzgVA8PJ3bWn1TG2S9Nxzz+niiy9WdHS0Lr74YkeGnrFgwQLZbDbTcmbmYABojT+zktmHAAQLf9eWABAsrM7Kuro601JfX+/xuLW1tbLb7W531YmPj3e7k84ZNTU1Hts3NTWptrbW4zZz5szRoEGDdP3117f3rQEAB3/XldxhAkCw8HdedhcMtgSCmGHxAgChKhiy8umnn9all16qrKwsZWVl6bLLLtP//M//mNq89957OnnypOP5L3/5S82ePVs5OTlKT0/XkSNHtH37dvXq1asTewogVPmztjwzU9uDDz6ot956S6NHj9b48eNVWVnpsf2ZmdpGjx6tt956Sw888IDuu+8+Pffcc442ZWVlmjJliqZOnap//OMfmjp1qm655Ra9/vrrpn1dcsklqq6udizvvPNOO3sPoLuxOit9/UL8zOxDrrMJdWT2ob1796qxsdHjNsw+BMAKXLcEAN9YnZWJiYnq3bu3Y1m8eHGbx7fZzF+kG4bhts5be0/rJWnJkiXauHGjnn/+ecXExLTZDwBoiz/rys64bnnmDhN/+9vfVFZWpqSkJGVlZenIkSMd6CEAtOBzeNcImtuIo4PaM9i4i/612NpxnLMeLO16LAZfA/g/dqPZ8bhJ9lbbhbn8LiHMKUjCbdb+ZsG5T80uAdasZtfmDhEK77Q+oeucf/752rBhQ5ttXG+LYLPZtGDBAi1YsMDn43BrhU5g+7+lrbrDaGV9R1/r5P+MzvWazW5zetz6Nm51W7jT4zCj9XY+d8rpWE77Mx3H5TW3/yRNzufivMMO9qkj2vrv2JHX2vqbCSLOM7VJUmFhobZt26aVK1d6/GLIeaY26ZsZgvfu3auCggLHbXELCws1duxY5efnS5Ly8/O1c+dOFRYWauPGjY59RUREMJtlVwqhz2iBmJWmz9vNrfeprc/lhnOfwi3I70AQ4H93iYmJpufz58/3WN91xuxDCQkJbtsw+xDOmkvINDvdUdTeo+W15nNcwinCabt682fb8K9anofXO+ebyz/w1sLKpU/OWWePbnnNfq7LZ+9op+dN5n2HnXL6LP51y2thjT72CUD35hINhlMGGjEt+Rh+TpOpXVhYSy7ZG80fiJtPOX3l19CSm6bPv1Krnxtda0Tn7cIaWtZHnHLJQ6ffbxgun9GberQ8tjuPtYtwyWWi0jJVVVWKjY11PI+OjvbYLi4uTuHh4W515LFjx9zqxzMGDBjgsX1ERIT69u1rWl9QUKBFixbppZde0mWXXdaRUwEkuVwHlGQ41Wcx5592PB7c9zNTu56RLT9iq/4q1vTav4/3djy2f+FUrDaYmsnW7Dmc3PoU1fI8vFdLKMb3PWlql3BunePxl43mf5uHj7f82O30Z06B6VIXu2U6Ol1nXLd8+umnTdusWbNGzz77rF5++WXdddddnXtCaF1Hv5/pwu9uWtOlWVlvfqNavc7ost65Zoz8omUfPT41N4yuc/qMHmXex6n+LZlYf75Tu2iX/3jhXfQfojO+77N5aIOAw4gMIIhxOx4A8A1ZCQDedUZt6ctsbZ01U1trbVz3+cEHH2jgwIFKTk7Wrbfeqo8//rh9bxyAbsfqrKyqqtLJkycdy5lB4q1h9iEAwYDrlgDgG6uzMjY21rS0NtgyKipKaWlpKi0tNa0vLS1VZmamx20yMjLc2m/fvl3p6emKjGwZhPH444/r4Ycf1osvvqj09PSzeXsAQJL/vuPhDhMAgg2fw7sGgy2BYGblHMBBOgsSAPiErAQA7zqhtvTl9mWdMVNbW22c9zly5EitX79e27Zt05o1a1RTU6PMzEwdP3687fcKQPdmcVb6+oV4V80+tH37dmYfAnD2uG4JAL7xY1bm5eXpySef1Nq1a3Xw4EHl5uaqsrJS2dnZkr65Q4TzDGvZ2dk6fPiw8vLydPDgQa1du1bFxcW6//77HW2WLFmiuXPnau3atRoyZIhqampUU1OjL7/8sv0dBIAzLM5KX34gLnXedUtX3GECgGX4HN4luI04AAAAAKBT+Hr7MqlzZmrzts/x48c7Hl966aXKyMjQsGHD9Pvf/155eXmtHhsA/MF59qFJkyY51peWlmrixIket8nIyNALL7xgWtfa7EOPPPKItm3bxuxDAAAA3cSUKVN0/PhxLVy4UNXV1UpNTVVJSYkGDx4sSaqurlZlZaWjfXJyskpKSpSbm6sVK1Zo4MCBWrZsmeO2uJJUVFSkhoYG3XzzzaZjzZ8/XwsWLOiS8wIAbxITE03PvWVUV9xhYseOHdxhAgCCBIMtgWBm5fS9TAMMIJRZlZdkJYBQ1gm15ZlZ2trSWTO1tdamtX1K0rnnnqtLL71UH3zwQZt9BtDN+bG2zMvL09SpU5Wenq6MjAytXr3abfahI0eOaP369ZK+mX1o+fLlysvL04wZM1RWVqbi4mJt3LjRsc8lS5Zo3rx5euaZZxyzD0lSz5491bNnz7M/TwDdE9ctAcA3fr5umZOTo5ycHI+vrVu3zm3dmDFjtG/fvlb3d+jQoQ71AwDaZHFW+voD8a66w8RLL73EHSYAWIPvxLsEtxEHAAAAAPiN80xtzkpLS5WZmelxm4yMDLf2rjO1tdamtX1KUn19vQ4ePKiEhISOnAoAdLopU6aosLBQCxcu1OWXX66///3vPs0+tGPHDl1++eV6+OGH25x9KCEhwbEUFBR0+fkBAAAAANDZzvxA/MzS2mDLzrpuKX1zh4mHH35YL774IneYAIAgw2BLIIgZhrULAIQqshIAvPNnbZmXl6cnn3xSa9eu1cGDB5Wbm+s2U9tdd93laJ+dna3Dhw8rLy9PBw8e1Nq1a1VcXKz777/f0WbWrFnavn27HnvsMb377rt67LHH9NJLL2n27NmONvfff7927typiooKvf7667r55ptVV1enu++++6zeSwChzd+1ZU5Ojg4dOqT6+nqVl5frmmuucby2bt067dixw9T+zOxD9fX1qqiocGTrGYcOHZJhGG4Lt3kEcDb8fd2yqKhIycnJiomJUVpaml599dU22+/cuVNpaWmKiYnR0KFDtWrVKtPra9as0ejRo9WnTx/16dNH119/vd544432dwwAXPi7tgSAYODPrOyM65ZLlizR3LlztXbtWscdJmpqavTll1+e9XsFoHujtuwa3EYcCGKGhbfjsey2PgAQgKzKS7ISQCjzZ205ZcoUHT9+XAsXLlR1dbVSU1N9mqktNzdXK1as0MCBA91masvMzNSmTZs0d+5czZs3T8OGDdPmzZs1cuRIR5tPPvlEt912m2pra9WvXz9dddVV2rNnj+O4AOAJtSUAeOfP2nLz5s2aPXu2ioqKNGrUKD3xxBMaP368Dhw4oKSkJLf2FRUVmjBhgmbMmKENGzZo165dysnJUb9+/Rz15Y4dO3TbbbcpMzNTMTExWrJkibKysrR//34NGjTIkvME0D1RWwKAd/7Mys64bul8hwln8+fP54ePAM4KtWXXYLBlqHD6OzfCnIYYh5ubGbaW12zNLv847C3Pbc6jlDs4Yrm1fdjstlbbuR3Kuf9O58W/awAdUW80Oh6fam55fKK52dTO+dk5LnnTK6zlf53RapnuP9LmErg+ajTsHvv3RXOTqd0pp4B0nZb6vLCWNeeEtfQp2hYpAPCFzaUIszW2hF/EaafHp1zatUSY7FHm15rObdlpc5RTmIabD9ZqXeey3nDazohqSeqwc815GRXV8rzZbk7MxlNOuXi6Jbedz/ebA7TSJ3SqnJwc5eTkeHxt3bp1buvOzNTWlptvvtntoqWzTZs2tauP6N4CMSvd+uT0eTusoWV9xFfmHYQ7vWa4lLFN5zg9jnF6IdLH/AbQbbSWA665Yu/Rkh/hA1pCcsSgo6Z2faK+djw++Hm86bUjR89vefJZy+fy8NMu1xmbPRdyhssHaXt0Szv7+S3146CBn5napfT5t+Px5w09TK/988jAln3UtISn6zVXm1O56vyeuWY4rLN06VJNmzZN06dPlyQVFhZq27ZtWrlypRYvXuzWftWqVUpKSlJhYaEkKSUlRXv37lVBQYHjS/Gnn37atM2aNWv07LPP6uWXXzbNZAT4yvQ9jiQjpqVo7NP/C8fjEf2PmNqdH/WV4/HBugGm1z74dz/H44bPnQq5NmpGE5f8Cmu5VKmoEy2v9Txqvpbao7Yl6Jp6mAP3i0Etmf11fMs+nGtOSW71L4BuzjmOXOq48J4tmfOdgS0ZmZPwiqndkIiWGQJf+DLF9NozusLx+GhDn5YXmlyGTpjjrtU+Kbolw+P7nnQ8vj3pTVOzG3sedDw+1NTT9FpR9H84Hu9taPkRcHOjy4UE5z4RnV3G6uuWhw4dsqhn6NYszso/fXGJ6bVNSnM8Nmel6/cpTuOMnDLKteZ0/vze49OWAOv7r6/M7d6ratnHebGm1yLSWurfz6NbLj40u1y3dH4/uIaJzsBtxIFgZtisXQAgVJGVAOAdtSUA+IasBADv/FRbNjQ0qLy8XFlZWab1WVlZ2r17t8dtysrK3NqPGzdOe/fuVWNjo8dtTp06pcbGRp1//vkeXwcAn1FbAoB3ZCUA+Ia87BLMbAkEMcP4ZrFqXwAQqqzKS7ISQCijtgQA31BbAoB3nVFb1tXVmdZHR0crOjratK62tlZ2u13x8ebZUePj41VTU+Nx/zU1NR7bNzU1qba2VgkJCW7bzJkzR4MGDdL111/f3tMBABNqSwDwjqwEAN+Ql12DmS0BAAAAAAAAAEBAS0xMVO/evR2Lp1uCn2GzmWfhMAzDbZ239p7WS9KSJUu0ceNGPf/884qJiXF7HQAAAAAAhC5mtgSCmfF/i1X7AoBQZVVekpUAQhm1JQD4htoSALzrhNqyqqpKsbGxjtWus1pKUlxcnMLDw91msTx27Jjb7JVnDBgwwGP7iIgI9e3b17S+oKBAixYt0ksvvaTLLrusI2cDAGbUlgDgHVkJAL4hL7sEM1sCAAAAAAAAAICAFhsba1o8DbaMiopSWlqaSktLTetLS0uVmZnpcb8ZGRlu7bdv36709HRFRkY61j3++ON6+OGH9eKLLyo9Pd2CMwIAAAAAAMGGmS2BIGYYNhlG67e/ae++ACBUWZWXZCWAUEZtCQC+obYEAO/8WVvm5eVp6tSpSk9PV0ZGhlavXq3KykplZ2dLkvLz83XkyBGtX79ekpSdna3ly5crLy9PM2bMUFlZmYqLi7Vx40bHPpcsWaJ58+bpmWee0ZAhQxwzYfbs2VM9e/a05DwBdE/UlgDgHVkJAL4hL7sGgy2BYMf0vQDgG/ISALwjKwHAN+QlAHjnp6ycMmWKjh8/roULF6q6ulqpqakqKSnR4MGDJUnV1dWqrKx0tE9OTlZJSYlyc3O1YsUKDRw4UMuWLdPkyZMdbYqKitTQ0KCbb77ZdKz58+drwYIFXXJeAEIYtSUAeEdWAoBvyMtOx2DLYOUyiNgIb/nXYkQ3tzSLsZvahYW1tGtuCDfvpN7prvKNLQew2Ts4Yrm5ZbuwppbV4afN+wtraHlsuNzY3h7j1N9op+3Czeng86Bq580YiA2EvEbDnIEnm1sC593Gcx2P3zmdaGp3qjnK8XhwVK3ptUuiahyPL4ho2V9PmW9dFW5zCbT/YzeaTc9PGS37+MQpK/c3DDK1O9wQ53h8jnNwSro0psrxeHjkV47HfcLMfYi0ueQ+AJzRbC6Mwutbnscca1nf60iTS7uW4urrOHPGfDWwJYPqz3OqVV3jsZWazLW+MyJb9hEZ25KDQ+PNOT28978dj79ojDG99taxlmz9/Fivlhfs5r53uP4FENo6OSsbere0s9vMx7KFtXKFzKVPYY0tj6PqWl4796i5Bu1R21In26PN+/hiUMuloq/jW15rci0lw7lqB8CJzanec8mL5nNbMueKxE8cjxdfsNXULjmyZXbA4tgBptdWNIxxPD5x6jzH47BGl7w0x13rfXK65tgn7gvH4/8cvNvUblrvlmsAFY1fml7LD/uh4/HrXwxrOdZp8yV3m90pL5kZosvk5OQoJyfH42vr1q1zWzdmzBjt27ev1f0dOnTIop6hW3OOAJdcijinpYa8YkDLYOAHB5hvcZ8U0ZKVm87tY3ptlVNWHj4V2fJCk8tXgU5ZaWvlsSSFOde7x1uy7Lx/nTDv7p/vtrTrY+6TbdSFjseNvVr6YTdfSpWcrhUQlQBMXDLB5lR39o782vF4SIS5VnPOy34RdabXosJb6lObBZnjvA/nfbse17lPkrm/zufifI58nw3AJxZkZXzkCdNrlmelU7Q5jx8K+9L8vbf9888dj90uR56Ob9mfc+3KZUp0MQZbAkGMWz0CgG+YMh0AvKO2BADfUFsCgHfUlgDgG2pLAPCOrAQA35CXXYPBlkAwM2TdKH1G+wMIZVblJVkJIJRRWwKAb6gtAcA7aksA8A21JQB4R1YCgG/Iyy7h+R6nAAAAAAAAAAAAAAAAAAAAkMTMlkCQs/3fYtW+ACBUWZWXZCWAUEZtCQC+obYEAO+oLQHAN9SWAOAdWQkAviEvuwIzWwIAAAAAAAAAAAAAAAAAALSBmS2BYGb832LVvgAgVFmVl2QlgFBGbQkAvqG2BADvqC0BwDfUlgDgHVkJAL4hL7sEgy2BYMZFSwDwDYUlAHhHbQkAvqG2BADvqC0BwDfUlgDgHVkJAL4hL7sEgy2DlGFzeR7V7Hgcfd5px+NB5580tesR0eh4XP1FL9Nrn3/Ws2V/Xzn9abgczNYsj1zXh9lbHkd81bKPmOPmf5XRJ1ue2yPNxzod1/K8vo9TuxjXg3vuE4Durd5oND3/uLElPP5wfKTj8UsV3za1a/g60vE4eVCt6bUpg/Y6Hn/vnPcdjyPDm0ztolv5X2y9YW5Xa28Jy11ft/Rj85F0U7uKI3GOx1E9zOd1fXJLP+7su9vxODXK3C7SFu6xTwC6J5tTSWazm1+L+Lrlca+jLbnV641KU7vmk3WOx9GXDDO91tSjp9PjlmLNcIlHI6yVT2yu653q3b7nfel4fNOAt03NpvT6wPG4yh5meu13Gut4/OqXLf1trnfJR+e6lg+UQLfmr6xsjjSHT2tRZHN5IayhZR/Rn7e8eN57X5m32/9Ryza9Y807GZnkeNgY2xLa9miXgztFrOs1CgBoTZiPxZVd5jrOcA4a5134Wqu5tnN67rxv1+O2xddzAYD2Cncq8nxPJam5taKsrQx02sTWVk3na71nmL8oshlkJYAOcP4s3mgOIPtnLR9Ot79ziePxKx9eZGoXFt6SR00N5mt/zV+1fAfkvH+b3fULeM/dszWZ2xlftHx2PvRRvONxfs2PTO3mRbVcWGh2uW7Z9HXLPmxft/TX9ViUoAAcAjArTeVohDmwGp2GJ528sOXxVwPPN/fphsyW/bl8dWPv0fK4qUfL/g2XY3GtEp2NwZZAMDNs1v2fgv/jAAhlVuUlWQkglFFbAoBvqC0BwDtqSwDwDbUlAHhHVgKAb8jLLsFgSyCIGcY3i1X7AoBQZVVekpUAQhm1JQD4htoSALyjtgQA31BbAoB3ZCUA+Ia87BrtuQMBAAAAAAAAAAAAAAAAAABAt8PMlkAwM/5vsWpfABCqrMpLshJAKKO2BADfUFsCgHfUlgDgG2pLAPCOrAQA35CXXYLBlkAwM2zfLFbtCwBClVV5SVYCCGXUlgDgG2pLAPCO2hIAfENtCQDekZUA4BvysktwG3EAAAAAAAAAAAAAAAAAAIA2MLMlEMRsxjeLVfsCgFBlVV6SlQBCGbUlAPiG2hIAvKO2BADfUFsCgHdkJQD4hrzsGgy2DFZh5r9sW4zd8Xhw388djyclvGVqNyDypOPxSycuMb22s2mY4/GX9ee2vNDk+q+oleliXaaRtTW2PI6qa3kce7jJ1O6cQy19aj432vTa58N7tnSjR8v+m6NcDh3Gv3QA37AbzY7Hpwy76bV/1g91PH7xgxTH4z6lPUztenzest0nVwwyvfbSmK8cj4dHH3U8Pj/slKldpC3cY//qDXMGHrG35NxLx1v69Mnr5uNe8GZLn77uY87KF8e2bHdZzyrH46GRH5ja9XB6b8JtTG4NoHW2lrhQWGNLnWV8/bWpXfOpluwLazDnm5rVacKdPuX1Cj9teq1P+DmOx18ZX5pe6xHeUqCGOe2jE7sKIIQFelY679vmclznPtmiIk2vOZ+LjYAE0AbnC++G0/XCsAbzdbrIT1suQb/++kWOx//xzoXmHTpd37M1mD+zhp9qeR7Z4NQH15xq5TZXYS7XNyNPtuzvy/f6OB7/pupGU7vFUU4HaDbvO8y5T6edzt8l6p37xJcVQDfnlAG2RnOm2I+3XO/761eXOh5v65FiamdzysrmBvP1R+N0y3Nbg1P22H27BWBzhDmkGnu1PD75rZbHXw0639QubEJmSx9cDmXv0bJPe4xTzRxuPhZ3KQQ6ie3/lra+6jVaWd/R1yyud8IazAeO/LSlBos91PJan/3m72hsp+odj78eas6tzy9sqU+/7u+cU64Hb+VkXOrCiC9anvc45tSnD8zb9/i45Qtz4xyX78QvaTl43ZCWc2yMNe+jOdLiN7gr/xZsanWYAeBXZKWkjmelqa5z6oZrbWn0avmuu1f/lu9u/iPR/H32Db3fcTw+1tTL9Nqm6isdj9+tGtDyQp35+qZrrX3W2pNz7X2ttb8Zrh8ENAZbAsHMkHUhS1gDCGVW5SVZCSCUUVsCgG+oLQHAO2pLAPANtSUAeEdWAoBvyMsuwWBLIJgZNut+8slPRwGEMqvykqzE/2fv78OjKu99j/8zSSAhmAwPaRLYgkGIPIgPiJsQtpZUJcaW0opV2dmd66JbA24O0mBbDhR7GFqFA0XkV9JdFW1hF6ic6sGtbncOcXvKr/4ITyrycDCtFjUIA1TCBCUkQOb3B82aWZPJzJCsycyavF/Xta6uWetea+5FMx+/s+aee4BkRm0JANGhtgSAyKgtASA61JYAEBlZCQDRIS+7Bb8hCgAAAAAAAAAAAAAAAAAAEAYzWwJ2xs/xAEB0mDIdACKjtgSA6FBbAkBk1JYAEB1qSwCIjKwEgOiQl92CwZaAnXHTEgCiQ2EJAJFRWwJAdKgtASAyaksAiA61JQBERlYCQHTIy27Bz4gDAAAAAAAAAAAAAAAAAACEwcyWgJ3xDXEAiA7f4gGAyKgtASA61JYAEBm1JQBEh9oSACIjKwEgOuRlt2CwpZ04AtaD5iRN633JWC/MPmWsf+uqOlO7QWlXGeuNlz4y7dvX5++M9S/SMkM/b7juBb3YUi76D0z70r+zz7EvTe0u/b8/Geup2dmmfX2+MtJYPzeol7F+obXj5/ZF2V8Ayak14L/8X7aag+nj8znGesrHfYz13DfrTe0u1h811gf0mWja9+exXzHWT+X6M+tCL3O2deRCUGVy6qL/HH/+3H/uAQfN7fq8sttYzxpytWmft3CIsf7xaP81fpn5J1O7/in+c6ZG1VsAycxUM6WZM6cloCQ7PdJfgzUNGGNql3rBf9z5fuYi7PxA/+NLffztfClRvkNrDSrqzvsL4GMn+xnray7eaWr2+yyvv78Xe5n2fXq6v7F+obG3se64GPRcvIkE8DeJkpUdvs8NanfJX+LqXL7/oBPF/UztMkb7a9xLvcwnb/qK/3FLdkCf0qLsE4AeyRFwry64turj8a8P+KDFWO+9x/yetfXsWWM99fqRpn0NN/nruC8H+evCi31MzeTr4M2u45K5T2lN/vW+x/2d7//+GVO7S4f891ZTsrJM+1r+/jpj/fSodGO9ub+pmXyBd+DJTiA5deI9ZEqLORB6NfqzzXnEv6/foS9M7RxfnjfWm4YPNO1ruM4fOE25/k5dygjqbmpAhx0dbJfUepX/c6fMXH8/pgwxf+709X7vG+uei/1M+353fIKx/v8+HeTf0Wh+v+64QEACCM0X9Jl4q/+Wnlqy/dlxbshVpnYpLf7PuptyzEXixYCPwU31oyO6972O4Hap/oaB5w5+Xvn8hWJrb/OFBV5L4DUGXz8AhBLPrOy4U0EhGvCZT9M5/3voD7x5pmap8r9Hbwx603/iC3//fS3+i3YEjR8CYo3BloCd+RzWfcLFJ2UAkplVeUlWAkhm1JYAEB1qSwCIjNoSAKJDbQkAkZGVABAd8rJbMNgSsDGHL/ovDkRzLgBIVlblJVkJIJlRWwJAdKgtASAyaksAiA61JQBERlYCQHTIy+7BxNMAAAAAAAAAAAAAAAAAAABh2G6w5b/+679q2LBhysjI0Pjx4/XHP/4x3l0C4sdn8XKFrvT1uH37do0fP14ZGRm69tpr9cwzz7Rr8/LLL2vMmDFKT0/XmDFjtHXr1ivvGCSRl4BJHLMSiY2sBAL00NqSHIiMfyMgSJxrS96LJy7yEggQ59oSiYusBIJQW6ID5CUQgKxEB8hKIAif8XRLDthqsOWWLVtUWVmpxYsX67333tPtt9+ue+65R59++mm8uwb0OFf6ejxy5Ii+/vWv6/bbb9d7772nH//4x5o3b55efvllo01tba0efPBBuVwuvf/++3K5XHrggQe0a9eu7rqspEFeAkBkZCWQOOJVW5IDkfFvBCQW3osnLvISACIjK4HEQm2ZuMhLIHGQlYmLrAQSR0/7jKdTgy3vuOMOLV26tN32hoYG3XHHHV3uVEdWr16thx56SA8//LBGjx6tNWvWaMiQIfrVr34Vs+cEENqVvh6feeYZDR06VGvWrNHo0aP18MMP65//+Z+1atUqo82aNWs0ZcoULVq0SKNGjdKiRYt05513as2aNd10VdaKV1ZK5CUAe6G2BBCv2tJOOUBWApB4Lx4J78MBIDrUlgAkastIqC0BSGRlNKgtAfS0z3g6NdjyD3/4g6qqqvTtb39bX375pbG9paVF27dvt6xzgVpaWvTOO++otLTUtL20tFQ7duyIyXMCic4hyeGzaLmC5+3M67G2trZd+7vvvlt79+7VhQsXwrax62s8HlnZdn7yEjCzLC/jfSFJitoSSAw9rba0Ww6QlUDiiFdtyXvxyHgfDiSOeNWWiA61JZA4qC0TF7UlkDjIysRGbQkkjnjkZU/8jKfTPyP+5ptvyuPxaOLEifr4448t7FJof/3rX3Xp0iXl5eWZtufl5cnj8YQ8prm5WY2NjaYFQHjBr5nm5uZ2bTrzevR4PCHbX7x4UX/961/DtunonHbQ3VkpXfn/P2QlgERAbQkkp0SuLTvzvPFGVgLJKZqslHgvHi07vA+XyEsA8UdtCSQnaktrUVsCyYmstB61JZCc+IwntLTOHjho0CBt375d//zP/6y///u/1+9//3uNHj3ayr6F5HCYx8/6fL5229osX7485HTFQNLwOS4vVp1L0pAhQ0yblyxZIrfbHfKQK3k9dtQ+ePuVnjPRxSsrpej/LclK9AhW5aVVmYt2bF1b+v62BB/mC3yiDrZ3dp/Ff4qtvcyPL2VdNNZTRp431gcNaDC165N2wVj/7KzTtO/86auMdd8X/rcdjgvm73s5WgMeBFxjygVTM6U0pRrraZ/5z3fp83RTu5NnBvj39TL/Q/X6iv9x6wD/k13KMP/D+zr9lbQORPv/Y2f2hfqb6ezfRw+tLe1Uf5KVV7gvWbMyXJ8yLxnrFwf7+9d3wBemdrlZXmO96aL5JI2n+xvrLacz/H04n2pq11GfOq07/xZ8IdpcCYtryyvJSon34pHY4X24xHtx9AAxqC1hLVvXlkAyobZMaLavLZPhvXi6+c1nc3//+96+t/gHSl2X+5mpXXZak7F+yDvItO9zz1eM9YuNvY11R3Mn34tf5e+Tr6DFWL/67lOmdtc7jxvrjRf7mPa9e/LvjPXmE9n+PpwLei9+yeJ/4O5+L8778E6fM9HZurYkKyVZlJXhPuP50p9nvY9kGutn3jC/Ht895e9Ha2/zc/mu9p8jPd//j3gxM+gzntTOhk0HuvsznlDHRyuOedmTPuPp1GDLtk6lp6dr06ZNeuKJJ1RWVqb//t//u6WdC5STk6PU1NR2o09PnjzZbpRqm0WLFumxxx4zHjc2Nrb7QwBsrStFaahzSaqvr1d2tr+IT09Pb9e0M6/H/Pz8kO3T0tI0cODAsG06Omeii0dWSlf+/w9ZiR7Bqry0uDbHZdSWQILoYbVlZ543nshKIIFYXFtGk5US78WjYZf34RJ5iR4gBrUlrENtCSQQasuERW0JJBCyMqFRWwIJJA552RM/4+nUnC1to0nbPP7449q0aZOeeuopSzoVSu/evTV+/HjV1NSYttfU1GjSpEkhj0lPT1d2drZpARBe8GsmVFh25vVYXFzcrv22bdt06623qlevXmHbdHTORBePrJSu/P8fshJAvFFbAskrkWvLzjxvPJGVQPKKJisl3otHwy7vwyXyEkB8UVsCyYva0jrUlkDyIiutRW0JJC8+4wmtUzNbHjlyRF/5yldM2+677z6NGjVKe/futaRjoTz22GNyuVy69dZbVVxcrOeee06ffvqpHnnkkZg9J5DQ4vgN8Uivx0WLFumzzz7Tv/3bv0mSHnnkEVVVVemxxx5TRUWFamtr9cILL+h3v/udcc7vf//7+upXv6oVK1boW9/6lv793/9db775pt5++22LLrJ7xSsrJfISaIeZLRMatSWQIHpgbWmnHCArgQQSx9qS9+Lh8T4cSCDMbJnQqC2BBEJtmbCoLYEEQlYmNGpLIIHEKS972mc8nRpsec0114Tcfv311+v666/vUofCefDBB/X555/rpz/9qY4fP66xY8fqjTfe6LA/QLJz+C4vVp3rSkR6PR4/flyffvqp0X7YsGF64403NH/+fP3yl7/U4MGD9Ytf/EL33Xef0WbSpEl68cUX9fjjj+snP/mJhg8fri1btqioqMiSa+xu8cpKibwEglmVl1ZlLsyoLYHE0BNrSzvlAFkJJI541pa8Fw+P9+FA4ohnbYnIqC2BxEFtmbioLYHEQVYmNmpLIHHEKy972mc8nRpsGU9z5szRnDlz4t0NAAr/ely/fn27bZMnT9a7774b9pzf+c539J3vfMeK7vV45CUAREZWAokjXrUlORAZ/0ZAYuG9eOIiLwEgMrISSCzUlomLvAQSB1mZuMhKIHH0pM94bDfYEkAAfo4HAKLDz4gDQGTUlgAQHWpLAIiM2hIAokNtCQCRkZUAEB3yslsw2BKwM25aAkB0KCwBIDJqSwCIDrUlAERGbQkA0aG2BIDIyEoAiA552S0YbGkngX/MreZdF1tSjfU/N37FWP/3viNN7fJ7eY313WeHm/Z5mzICTugI/bzhuucwP25N8x94sa9/Z9PgvqZ2mS3X+Y/pm27a1zTQ/yd6qXfAjpTwzw2g50qRPxD6ppjDoSDjr8Z6a0GTsX7yriGmdn0aBhvrp8eaz3HTwFPG+lfSGo31XoouiILbBZ6jMODc74/tbz7u2xOM9ab+qaZ9gdcSeI3B158SZR8B9BCBkZBmLvh6ZbcY618r+LOx/uO8N03trk67yljfdHagad+vjkw21j+7OMC/41Jw0Rg6mxxB21Ob/I8zPf7+fmXvGfPp3j/sP6af07Tv3D/4687Pr+9lrJ8PflfUy39+6kygh0uUrOwojFKC3rBn+G8WDM49Y6z/y7Dtpmb/lPW5sX704hemfctO3GWsv3nRf0/h4sUMUztduPL7BgCSly/gXp0v3RwKX17tX28c4a/BWh8YbT5JQKY5Wsw3/1LP+TMnpSWgXdA90o7y0pdq7lNzQKQ15fmPOTGpn/m43n/vfxBUn6ac8/cx9bz//CkXO+6Tg7wEklMn3je2BmXl+Xx/oDUV+NdPft1cgzlS/J+htLaYz+E77w8gR0tA9gTXlqaDAs59MSjnvP43y+f/2s9Y/893Jpra/Z8L/sfBMXypj/8JUgMuJTiXO/Xem/frQM8Q9Jmwo7c/I/Ou8r+fvd1ZZ2qXm3bWWL8UdJJjjdnG+tkv/PVpu2LN0UHQBLcLqGP7ZDYb66OcJ0zNpjgPGesnL2aZ9n12zn8fs6HBfx9B582fB+lS6C4B6OHimZUdFWVBBZ4jIL/SzvnX+/zVHGx9jjT4T5FpHj/UnO3v0/kBAfVu0G1LX1B0AlZjsCVgYw6fdTdpudkLIJlZlZdkJYBkRm0JANGhtgSAyKgtASA61JYAEBlZCQDRIS+7R0rkJgAAAAAAAAAAAAAAAAAAAD0XM1sCduZzWPfblvxGJoBkZlVekpUAkhm1JQBEh9oSACKjtgSA6FBbAkBkZCUARIe87BYMtgTszPe3xapzAUCysiovyUoAyYzaEgCiQ20JAJFRWwJAdKgtASAyshIAokNedgt+RhwAAAAAAAAAAAAAAAAAACAMZrYEbMzhu7xYdS4ASFZW5SVZCSCZUVsCQHSoLQEgMmpLAIgOtSUAREZWAkB0yMvuwcyWgJ35LF4AIFnZICsbGhrkcrnkdDrldDrlcrl05syZsMf4fD653W4NHjxYffr0UUlJiQ4dOtSuXW1tre644w717dtX/fr1U0lJiZqammJ0JQBsi9oSAKJDVgJAZNSWABAdshIAIiMrASA65GW3YGZLu2p1mB76zqca65983t9Y/71vvKldn7QLxvrxs1mmfV82ZvgfXAw4v8/8XB0KGtrs6+U/riXbv73xGvOfXXO/Acb6pV7m5zqf4398KcN/fl8Kr2wAoaU6/N8jyHSkmvbdmF5vrJcVHjbW30y7ztTu86Zexvqwv/OY9t010H/c36V+YaynO3qb2qUodHamO8wZGHiOwHN/XtTX1O7I1TnGeu8+5kFyZcP+ZKwHXmPw9Qf+2yDxlJeX6+jRo6qurpYkzZo1Sy6XS6+99lqHx6xcuVKrV6/W+vXrdd111+mJJ57QlClTVFdXp6ysy/+dr62tVVlZmRYtWqS1a9eqd+/eev/995WSwt8DOtYaUP81XfJn4ulWc4b1vXTOWD976e9M+y5FW0N2RsCfr6+3uU8pmZnGuqNPH9O+1oBa08dLAEAXJXpWBp777KUM076GgD4F9zfwWlpjmeUAbM8UEQH3BVvNb491YeBFY714zIfG+pNXm9/rDOt1lbH+nHewad+v/vRVY937qdNYTztrLupSLoa+ZxgUdbqY1WqsO4d6jfV/ue7/a2o3y3nMWD9y4QvTvsVHv2ms1/6/EcZ6r8+D6tOWgHuaAfcKmCUC6IECP3bpZQ6B1P7NxvqUwg+M9R/nvWlqd3WaPytfPNvftO9fPy4x1uuP+T930RfmXHJcDF3jpQRtT/vC//iqo/7+5uw9bWrXut/f39R+TtO+c//gv+/617H+OrPZ3HUp4N+DEhSwkONvS3DdEfg683WwvbP7LK5xUprNT+w4nm6sH/lLgbG+sqnA3O6Sfz24Pr3Y19/JNH80yZca9Fl3B3mUcimoT+f9Odt8qp+xXrN7gqndf7X4H/vMH9/oUsBtzNQ+AZmYFl2fOq07/xYcan8skAjISkkWZWWYevdCwHiflq/4189OuGhql9bb/xl56yXze/6LTf62jiZ/kLarb61+v30lOXel+zr6m+GeQUJjsCVgZz4Lb8wS1gCSmVV5GaOsPHz4sKqrq7Vz504VFRVJktatW6fi4mLV1dVp5MiR7bvi82nNmjVavHixpk+fLknasGGD8vLytHnzZs2ePVuSNH/+fM2bN08LFy40ji0sLIzNhQCwN2pLAIhOgteWAJAQqC0BIDrUlgAQGVkJANEhL7sF87kAAADEWW1trZxOpzHQUpImTpwop9OpHTt2hDzmyJEj8ng8Ki0tNbalp6dr8uTJxjEnT57Url27lJubq0mTJikvL0+TJ0/W22+/HdsLAgAAAAAAAAAAAAAgyTDYErAzn8ULACQri7OysbHRtDQ3N6srPB6PcnNz223Pzc2Vx+MJcYSM7Xl5eabteXl5xr6//OUvkiS3262KigpVV1frlltu0Z133qk///nPXeozgCREbQkA0SErASCyONeW//qv/6phw4YpIyND48eP1x//+Mew7bdv367x48crIyND1157rZ555pl2bV5++WWNGTNG6enpGjNmjLZu3XrlHQOAYNSWABAZWQkA0SEvuwWDLQE74wNxAIiOxVk5ZMgQOZ1OY1m+fHnIp3W73XI4HGGXvXv3SpIcDkf7bvt8IbcHCt4feExra6skafbs2fre976ncePG6emnn9bIkSP161//Oux5AfRA1JYAEB2yEgAii2NtuWXLFlVWVmrx4sV67733dPvtt+uee+7Rp59+GrL9kSNH9PWvf12333673nvvPf34xz/WvHnz9PLLLxttamtr9eCDD8rlcun999+Xy+XSAw88oF27dl1Z5wAgGLUlAERGVgJAdMjLbpEW7w4AAADYTX19vbKzs43H6enpIdvNnTtXM2bMCHuugoIC7d+/XydOnGi379SpU+1mrmyTn58v6fIMl4MGDTK2nzx50jimbfuYMWNMx44ePbrDD5kAAAAAALCz1atX66GHHtLDDz8sSVqzZo3+z//5P/rVr34V8suSzzzzjIYOHao1a9ZIuvyeee/evVq1apXuu+8+4xxTpkzRokWLJEmLFi3S9u3btWbNGv3ud7/rngsDAAAAAABxx2BLwMYcvsuLVecCgGRlVV62nSM7O9s02LIjOTk5ysnJidiuuLhYXq9Xu3fv1oQJEyRJu3btktfr1aRJk0IeM2zYMOXn56umpkbjxo2TJLW0tGj79u1asWKFpMsDOQcPHqy6ujrTsX/60590zz33ROwXgJ6F2hIAomN1bQkAySgWtWVjY6Npe3p6ersvP7a0tOidd97RwoULTdtLS0u1Y8eOkOevra1VaWmpadvdd9+tF154QRcuXFCvXr1UW1ur+fPnt2vTNkATADqL2hIAIiMrASA65GX34GfEAQAA4mz06NEqKytTRUWFdu7cqZ07d6qiokJTp07VyJEjjXajRo3S1q1bJV3++fDKykotW7ZMW7du1cGDBzVz5kxlZmaqvLzcaPOjH/1Iv/jFL/TSSy/pww8/1E9+8hN98MEHeuihh+JyrQAAAAAAdMaQIUPkdDqNJdQslX/961916dKldr8SkZeXJ4/HE/K8Ho8nZPuLFy/qr3/9a9g2HZ0TAAAAAAAkJ2a2tKl2o4hb/ONmm89kGOtHzvcyH5fiP7C1JdV8jmb/ORwXHf711uj65AsautsacPqLff3P25TqMLVr7ud/HHyOSxkB/e0dsMN8CgAIKd1hzsBre5031h8YuMtYH933mKnduYDAuab3X037ru/tv4mek+oPunSH+T+pqY7Q32dID/pPb07qJWP9H/p8ZKz3G/qlqd0n+f7ZETNTWkz7bsioN9YDrzHdkSHYx6ZNmzRv3jxjNo1p06apqqrK1Kaurk5er9d4vGDBAjU1NWnOnDlqaGhQUVGRtm3bpqysLKNNZWWlzp8/r/nz5+v06dO66aabVFNTo+HDh3fPhSFxBdaTl8y7Lp3zZ9X7Jwcb6/8f3WVqlxWQOR94zR88fn7mKv+DgFpVrdEVcr4Uc8F7KWDCmub+/nOcGdnX1K7PwOsDjjE/19nB/uu62CfguYLKYh+1JoA28crKaL85HObeQOC5X0m/2dTsg6ZBxvrZC+aaMfBaAq/REXT9UfcRAAK0RnlTL1XmG5KOwJuhgaeItm4LbhfwOPDcwc8bTrTXAuvU19ebfmUieFbLQA6H+f8fn8/Xbluk9sHbr/ScQGddCnhTGn0qSSkdTT8TLgMDnyBcfRdt7Rd0T9THawRAJ5hKvwvmHElv8D8eeOiisd73//dnU7tLDQ3GesrYUaZ9n9/a31j/Yoj/fBeuklla6PAL/Bxdknp94X98Vb3/mIF7T5vatR78wFhP7d/ftO/Lfyj09+96/3vxZnMzqZf//NzDBHq2RMzKwPE+vuAMvcrfj4K/83/+/i/X/MHU7IGr/J+DfnrxC9O+Jz1TjPW3PvRPVnOpwfze0PTvwT1MxACDLQE788m6/zjwHxkAycyqvIxhVg4YMEAbN24M//Q+cwccDofcbrfcbnfY4xYuXNjuJ9QAoB1qSwCIjg1qSwCIuxjUltnZ2abBlqHk5OQoNTW13YyTJ0+ebDczZZv8/PyQ7dPS0jRw4MCwbTo6JwBEjdoSACIjKwEgOuRlt+BnxAEAAAAAAAAAgO317t1b48ePV01NjWl7TU2NJk2aFPKY4uLidu23bdumW2+9Vb169QrbpqNzAgAAAACA5MTMloCNOXwhflK+C+cCgGRlVV6SlQCSGbUlAESH2hIAIotnbfnYY4/J5XLp1ltvVXFxsZ577jl9+umneuSRRyRJixYt0meffaZ/+7d/kyQ98sgjqqqq0mOPPaaKigrV1tbqhRde0O9+9zvjnN///vf11a9+VStWrNC3vvUt/fu//7vefPNNvf3229ZcJIAei9oSACIjKwEgOuRl92CwJWB3hBwARIe8BIDIyEoAiA55CQCRxSkrH3zwQX3++ef66U9/quPHj2vs2LF64403dM0110iSjh8/rk8//dRoP2zYML3xxhuaP3++fvnLX2rw4MH6xS9+ofvuu89oM2nSJL344ot6/PHH9ZOf/ETDhw/Xli1bVFRU1O3XByAJUVsCQGRkJQBEh7yMOQZbAgAAAAAAAACApDFnzhzNmTMn5L7169e32zZ58mS9++67Yc/5ne98R9/5znes6B4AAAAAALApBlsCduaTdaPSGd0OIJlZlZdkJYBkRm0JANGhtgSAyKgtASA61JYAEBlZCQDRIS+7BYMtARtz+C4vVp0LAJKVVXlJVgJIZtSWABAdaksAiIzaEgCiQ20JAJGRlQAQHfKyezDY0q6C/rAdlxz+B+dT/OsXUkztWgNeEY5Wh2mfAs5hyQsnxX+S1l7+zT5zl+ToE7Av6BS+1NDn8wV1PWqdPQ6ALfVypJoeO1N6G+s39DpnrA9JPWxq1xqwnhmUG1kp/v90pjv84ZbqCAq3DgS3y5S/T9ekXTDWB6R8Zmo3Pt3/OPiZ+qX4t2QGXGPw9QNAR9rVhc3+/Gg4lWWs//HL4aZmKan+xLzQYn5r0fql/7HjQifqzKAu+QJO35IdUGemmlPxXJ7/sS8oBi9m+tcvpQd0JIV3jQAi69asDH6uDmKqXbsLAauN/rrwz5dyTc0+/usAfx8umXP0wjl/jesIuMZ2zwUAgQJu1jkumUMr5Ut/lrxbf7Wx/qPWb5va9e/dZKwfbsgz7Wv4qz9nU88HPld03QtulxJwjsBz/6b3JFO7nf1P+Nu19DHt2//ZYP/5Aq6xXZ86fSMTQNIJjMegrLh4zl8X7vEMNdaXtpaZ2g3o/aWxfrgx37TveEO2/0FAHWe62RnUD1NEBd10bA1433x+oL/hmbH9TO365N9qrDf1MZ/k7N/5ryvwPXnw+3WiEkCHgt8eB8TMpYyAurBftqldYMxcyuxl2tca8NbcivwJPEfguVuDnje1f39jPbi/gddi+iydfAQQDSuy8qrepn2WZ2VADdpyyf/MJy70M7X79KL/M/GPL15l2ue94H9f7gvsFB/xoJsx2BKwM36OBwCiw5TpABAZtSUARIfaEgAio7YEgOhQWwJAZGQlAESHvOwWDLYEbIyf4wGA6DBlOgBERm0JANGhtgSAyKgtASA61JYAEBlZCQDRIS+7R3S/eQoAAAAAAAAAAAAAAAAAANBDMbMlYGf8HA8ARIcp0wEgMmpLAIgOtSUAREZtCQDRobYEgMjISgCIDnnZLZjZEgAAAAAAAAAAAAAAAAAAIAxmtgTsjG+IA0B0+BYPAERGbQkA0aG2BIDIqC0BIDrUlgAQGVkJANEhL7sFgy0BG3P4Li9WnQsAkpVVeUlWAkhm1JYAEB1qSwCIjNoSAKJDbQkAkZGVABAd8rJ7MNgyWQT8oTsuOfwPWs3NHHKoQxa/WHyBT2VaNz9RuKf1hekuAFypdEcvYz0tJdVYz0y51OExKUoJeuwPplRHSnDzK9bL4e9H4LnTU3uZ2rUGB3qANPnPYUWfAPRAQQWZ40JgPenPmAstHWeMo9VcuDkudbAvypqzXR2Y6j/wUrp/Z2ua+YTh3gD6UgPX/Q2pOQFEJQGzsl2fAu8HNPv74bvY29SuOcVca5rOcdF/DtP5uMEGIEhg3RVYTzmC3mKnNvl3XvJkGuvvNA4zNwys65rNWZr6pf9xanNATgW/Ve6gsHO0mkMs8Bw67b9F/llzjqndZ8cG+B9cNJ875VzAe/GmwOwM2YXL+8hSAH8TXBfqvD9TGk5mGevbvxhhapaS4g++SxdSTftaz/nzLLBWbfdcHUkxh1RrL/9xLf38+xp7mzP6i7/z15o+c5d0sY9//VJGwPlTCEQAHTOVdEFvsS/2Dcijof7QuZgxyNQutcX/uDnbnINNXwmoTwOyyRflxyvB7QLPEXjuz2+8ytQuvWCk/xjz23Sdy/WfNPAag5+L+5gA2sQtK1ODxvsEHha461JQYDX7+3Hic6ex/qLGm5pt71torH9xId2075PP/e/RL30RUPu2uzcgIKYYkQHYmc/iBQCSFVkJAJHZpLZsaGiQy+WS0+mU0+mUy+XSmTNnwh7j8/nkdrs1ePBg9enTRyUlJTp06JCpTXNzsx599FHl5OSob9++mjZtmo4ePWpqU1BQIIfDYVoWLlxo9SUCSHQ2yEoAiDub1JYAEHdkJQBEZpOsjMV9y9OnT+vRRx/VyJEjlZmZqaFDh2revHnyer2xvRgA9mSTvLQ7BlsCdsZNSwCIDlkJAJHZpLYsLy/Xvn37VF1drerqau3bt08ulyvsMStXrtTq1atVVVWlPXv2KD8/X1OmTNHZs2eNNpWVldq6datefPFFvf322/riiy80depUXbpknp7qpz/9qY4fP24sjz/+eEyuE0ACs0FWAkDc2aS2BIC4IysBIDKbZGUs7lseO3ZMx44d06pVq3TgwAGtX79e1dXVeuihh2J7MQDsySZ5aXcMtgQAAAAA2MLhw4dVXV2t559/XsXFxSouLta6dev0+uuvq66uLuQxPp9Pa9as0eLFizV9+nSNHTtWGzZs0Llz57R582ZJktfr1QsvvKCnnnpKd911l8aNG6eNGzfqwIEDevPNN03ny8rKUn5+vrFcddVVoZ4WAOKK2TQAAAAAAOg+sbpvOXbsWL388sv65je/qeHDh+uOO+7Qk08+qddee00XL17szksEAPwNgy0BG3P4rF0AIFmRlQAQmR1qy9raWjmdThUVFRnbJk6cKKfTqR07doQ85siRI/J4PCotLTW2paena/LkycYx77zzji5cuGBqM3jwYI0dO7bdeVesWKGBAwfq5ptv1pNPPqmWlhYrLxGADSR6VkrMpgEg/uxQWwJAIiArASAyq7OysbHRtDQ3N3e5j7G6bxmK1+tVdna20tLSutxvAMmF2rJ7MNgSAAAAABATVt+49Hg8ys3Nbbc9NzdXHo+nw2MkKS8vz7Q9Ly/P2OfxeNS7d2/179+/wzaS9P3vf18vvvii/u///b+aO3eu1qxZozlz5nTpmgDAasymAQAAACsxazqAZDNkyBAj05xOp5YvX97lc8bqvmWwzz//XD/72c80e/bsLvYYANBZDLYE7Mxn8QIAyYqsBIDIYlBbRnvj0u12y+FwhF327t0rSXI4HO277vOF3B4oeH80xwS3mT9/viZPnqwbb7xRDz/8sJ555hm98MIL+vzzz8OeB0CSSfDaktk0ACQE7lsCQHRskJXMmg4g7izOyvr6enm9XmNZtGhRh0+dSPctGxsb9Y1vfENjxozRkiVLwp4TQA9lg9oyGXAnFLAxK6fvZRpgAMnMqrwkKwEks1jUlvX19crOzja2p6enh2w/d+5czZgxI+w5CwoKtH//fp04caLdvlOnTrX7Bnib/Px8SZe/KT5o0CBj+8mTJ41j8vPz1dLSooaGBtPslidPntSkSZM67NPEiRMlSR9++KEGDhwYtv8AkofVtWVjY6Npe3p6eod5GQ2rZ9P45JNPQh7DbBoAwuG+JQBEJ9HvW7bNmr5z507jyzzr1q1TcXGx6urqNHLkyHbHBM+aLkkbNmxQXl6eNm/erNmzZxuzprcZPny4nnzySX33u9/VxYsX+TIPABOrszI7O9t0zzKceN+3bHP27FmVlZXpqquu0tatW9WrV6+o+g+gZ0n02jJZUKkmuwR8AfjCf3HDWt35XABsJdXhn9w5NUEmejb3qd3e7uwKgM4IV3fFYl8sBTyv45Ij5LpkruvavfGyuO+mGjI14ORBEe4LfN4wtWC31qQd/VvE6m8mgd4DRHvjMicnRzk5ORHbFRcXy+v1avfu3ZowYYIkadeuXfJ6vR0Oihw2bJjy8/NVU1OjcePGSZJaWlq0fft2rVixQpI0fvx49erVSzU1NXrggQckScePH9fBgwe1cuXKDvvz3nvvSZLpZig64FDyvT9LwKzsqE9qDWoXMDtC2BtnCZQnlnIE/W+cDRkyxPR4yZIlcrvd7dq53W4tXbo07Ln27Nkjidk0EGdBhVbKBX+YOFr9+3znzbemTWVcUP44LgWsB2ZatEVdUDvHJf8TpJ7370u5YH7v7XP4Hwc/k6lPAevdW2gCsK3gnLsYkB3n/NnT2mzOpUuO0Jl6+bFC74uypmsXXwHvvS+l+3e29jKfMDCz25W7gd1P8e8lKmPH6i/yRJo1PdRgy0izpnf0ZR1mTUdIKeZkCcyj5oH+fReuMt8kDMxEX9Cf1KV0/3GtgfuCnqujrHIEtWvt5W94ITvg3OnmE5wLyHpf0D3N1oA+XerdcZ/Q/eJ931K6nO1333230tPT9eqrryojI8OCK4Oho3vqVt/Xj6XuzMoo67h29xxb/AdeavQPFj52foCp2fG0fv4+BdW7CqiNHQHnC66L46YzfxvEvC1RrQJ2ZuWH6YQ4gGRmVV6SlQCSmQ1qy9GjR6usrEwVFRV69tlnJUmzZs3S1KlTTR/wjBo1SsuXL9e9994rh8OhyspKLVu2TIWFhSosLNSyZcuUmZmp8vJySZLT6dRDDz2kH/zgBxo4cKAGDBigH/7wh7rhhht01113Sbr8AdPOnTv1ta99TU6nU3v27NH8+fM1bdo0DR06NDYXDCAxWVxb2mUW4DbMpgEgKjaoLQEgIVhcW0b7RZ5oMWs6gIRgg894YnXf8uzZsyotLdW5c+e0ceNGNTY2GgPrv/KVryg1lclaAASwQV4mAwZbAnbGTUsAiA6FJQBEZpPactOmTZo3b54xQ8a0adNUVVVlalNXVyev12s8XrBggZqamjRnzhw1NDSoqKhI27ZtU1ZWltHm6aefVlpamh544AE1NTXpzjvv1Pr1640blunp6dqyZYuWLl2q5uZmXXPNNaqoqNCCBQtid7EAEpPFtaVdZgGWmE0DwBWwSW0JAHEXpy/yMGs6AFuxyWc8sbhv+c4772jXrl2SpBEjRpjOdeTIERUUFMTwigDYjk3y0u4YbAkAAAAAsI0BAwZo48aNYdv4fOY7AQ6HQ263O+xsHhkZGVq7dq3Wrl0bcv8tt9yinTt3XnF/AaC7MZsGAABAzxXtF3mYNR0ArBeL+5YlJSXtjgEAxFdKvDsQjY8//lgPPfSQhg0bpj59+mj48OFasmSJWlpa4t01IK4cFi+wP/ISCI2sRCCyEgiN2hKByEqgY3bIyk2bNumGG25QaWmpSktLdeONN+q3v/2tqU2o2TQqKys1Z84c3Xrrrfrss89CzqZx4MABjRgxQoMGDTKW+vr6GF5NYiMvgdCoLRGIrAQ6Fq+szMnJ0ahRo8IuGRkZplnT21zJrOlt2mZNDzymsbFRpaWl6t27N7Om/w15CYRGXYlAZCXQMfKye9hiZssPPvhAra2tevbZZzVixAgdPHhQFRUV+vLLL7Vq1ap4dw8AEgZ5CQCRkZUAEBlZCdgbs2l0H/ISACIjKwH7Ytb07kVeAkBkZCWAeLPFYMuysjKVlZUZj6+99lrV1dXpV7/6FWGJns33t8Wqc8H2yEugA1blJVmZFMhKoAPUlghAVgJhUFsiAHkJdIDaEgHISiAMG9SWmzZt0rx581RaWipJmjZtmqqqqkxtQs2a3tTUpDlz5qihoUFFRUUhZ02XpBEjRpjOdeTIERUUFMTughIYeQl0wAZZie5DVgJhkJfdwhaDLUPxer0aMGBA2DbNzc1qbm42Hrd9IwpIFg7f5cWqcyE5RcpLshI9gVV5SVYmL2pLgNoSkZGVwGXUloiEvASoLREZWQlcZofaklnT44u8BOyRlYgvshK4jLzsHrYcbPnRRx9p7dq1euqpp8K2W758uZYuXdpNvULCcMS7A0DiiCYvyUoAPZ0ta8twb3KsroXCPFcivNnyBV8vtSAQEzHLyo5es+Fey4n4Ok/wrAzuX0L0KVqd/VtIxL8T9Ai2rC0tEJgr7eqzgA2OiwHHXLqCMGp30sj9CHt4YJ8uBRzf2n19AnqynpqVYQVkheNSQL60mps5whU5FueNKeZSA06eEv3TRhmV0aPGQw/T5by0cqbpOGmXIwF5dCndv7m11xWcI6BA8wVlWlf71BoY4UEjMcLVhb6UrvXJFpLg7xGJyTa1ZQz//hMxK9vdjwyscQOf7ELQEztS/avB5wwIWUdr8E4LhS1wY/i8sI24/qfa7XbL4XCEXfbu3Ws65tixYyorK9P999+vhx9+OOz5Fy1aJK/Xayz19fWxvByg+/ksXpCwYpmXZCV6BLKyR6C2BLqI2rJHICsBC5CVPQJ5CXQRtWWPQFYCFiArewTyEugisrJHICsBC9ggLxsaGuRyueR0OuV0OuVyuXTmzJmwx/h8Prndbg0ePFh9+vRRSUmJDh06ZGrT3NysRx99VDk5Oerbt6+mTZumo0ePGvs//vhjPfTQQxo2bJj69Omj4cOHa8mSJWppabnia4jrzJZz587VjBkzwrYpKCgw1o8dO6avfe1rKi4u1nPPPRfx/Onp6UpPT4/YDrA1isIeIZZ5SVaixyAvkx61JWABsjLpkZWARcjLpEdeAhYgK5MeWQlYhLxMeuQlYAGyMumRlYBFEjwvy8vLdfToUVVXV0uSZs2aJZfLpddee63DY1auXKnVq1dr/fr1uu666/TEE09oypQpqqurU1ZWliSpsrJSr732ml588UUNHDhQP/jBDzR16lS98847Sk1N1QcffKDW1lY9++yzGjFihA4ePKiKigp9+eWXWrVq1RVdQ1wHW+bk5CgnJyeqtp999pm+9rWvafz48frNb36jlJRknT8bANojLwEgMrISACIjKwEgOuQlAERGVgJAdMhLAIiMrASS3+HDh1VdXa2dO3eqqKhIkrRu3ToVFxerrq5OI0eObHeMz+fTmjVrtHjxYk2fPl2StGHDBuXl5Wnz5s2aPXu2vF6vXnjhBf32t7/VXXfdJUnauHGjhgwZojfffFN33323ysrKVFZWZpz32muvVV1dnX71q1/Za7BltI4dO6aSkhINHTpUq1at0qlTp4x9+fn5cewZEF8O3+XFqnPB/shLIDSr8pKsTA5kJRAatSUCkZVAx6gtEYi8BEKjtkQgshLoGLUlApGXQGhkJQKRlUDHrM7LxsZG0/auzhBbW1srp9NpDLSUpIkTJ8rpdGrHjh0hB1seOXJEHo9HpaWlpn5MnjxZO3bs0OzZs/XOO+/owoULpjaDBw/W2LFjtWPHDt19990h++P1ejVgwIArvg5bDLbctm2bPvzwQ3344Ye6+uqrTft8Pv6LiB7MJ+umAOallBTIS6ADVuUlL6OkQFYCHaC2RACyEgiD2hIByEugA9SWCEBWAmFQWyIAeQl0gKxEALISCMPivBwyZIhp85IlS+R2uzt9Wo/Ho9zc3Hbbc3Nz5fF4OjxGkvLy8kzb8/Ly9Mknnxhtevfurf79+7dr09F5P/roI61du1ZPPfXUFV+HLebSnTlzpnw+X8gFAOBHXgJAZGQlAERGVgJAdMhLAIiMrASA6JCXABAZWQl0n/r6enm9XmNZtGhRyHZut1sOhyPssnfvXkmSw+Fod7zP5wu5PVDw/miO6ajNsWPHVFZWpvvvv18PP/xw2HOEYouZLQGExs/xAEB0+IkJAIiM2hIAokNtCQCRUVsCQHSoLQEgMrISAKJjdV5mZ2crOzs7Yvu5c+dqxowZYdsUFBRo//79OnHiRLt9p06dajdzZZv8/HxJl2evHDRokLH95MmTxjH5+flqaWlRQ0ODaXbLkydPatKkSabzHTt2TF/72tdUXFys5557LuK1hWKLmS0BAAAAAAAAAAAAAAAAAEDiyMnJ0ahRo8IuGRkZKi4ultfr1e7du41jd+3aJa/X225QZJthw4YpPz9fNTU1xraWlhZt377dOGb8+PHq1auXqc3x48d18OBB03k/++wzlZSU6JZbbtFvfvMbpaR0btgkM1uiawJnW43nN0HCzwybvHyy7t+db/IASGZW5SVZCSCZUVsiGfTU94bJwE7/31FbAmGFm0HB5+jogfXPFa5dh0/dyT4xQ04I1JaANRLw79+C+I6enWrEzqK2RDx09PcS7u+os/tiyJcSuJ4YLwKfacyGuU+J0cMgdvlbICuBTkvErHS0mh7FqxtmifFP03UJnpejR49WWVmZKioq9Oyzz0qSZs2apalTp2rkyJFGu1GjRmn58uW699575XA4VFlZqWXLlqmwsFCFhYVatmyZMjMzVV5eLklyOp166KGH9IMf/EADBw7UgAED9MMf/lA33HCD7rrrLkmXZ7QsKSnR0KFDtWrVKp06dcp4vrbZM6PFYEvAxvg5HgCIDj8xAQCRUVsCQHSoLQEgMmpLAIgOtSUAREZWAkB07JCXmzZt0rx581RaWipJmjZtmqqqqkxt6urq5PV6jccLFixQU1OT5syZo4aGBhUVFWnbtm3Kysoy2jz99NNKS0vTAw88oKamJt15551av369UlNTJUnbtm3Thx9+qA8//FBXX3216fl8viu7YAZbAgAAAAAAAAAAAAAAAACAmBkwYIA2btwYtk3w4EeHwyG32y23293hMRkZGVq7dq3Wrl0bcv/MmTM1c+bMK+1uSAy2BOyMn+MBgOgk+JTpAJAQqC0BIDrUlgAQGbUlAESH2hIAIiMrASA65GW3YLAlYGfctASA6FBYAkBk1JYAEB1qSwCIjNoSAKJDbQkAkZGVABAd8rJbpMS7AwAAAAAAAAAAAAAAAAAAAImMmS0BG3P4Li9WnQsAkpVVeUlWAkhm1JYAEB1qSwCIjNoSAKJDbQkAkZGVABAd8rJ7MLMlgJhraGiQy+WS0+mU0+mUy+XSmTNnwh7j8/nkdrs1ePBg9enTRyUlJTp06JCpzXPPPaeSkhJlZ2fL4XBEPCcAAAAAAAAAAAAAAAAAdAaDLWEdR5jFDue3I5/FS4yUl5dr3759qq6uVnV1tfbt2yeXyxX2mJUrV2r16tWqqqrSnj17lJ+frylTpujs2bNGm3PnzqmsrEw//vGPY9d5AMnBBlkJWIa/V3SWTWpLAIg7shLotLYZFqxa7N6PpEZtCaCzetpnP2QlAERGVgJAdMjLbsHPiAM25vD55PBZk3JWnSfY4cOHVV1drZ07d6qoqEiStG7dOhUXF6uurk4jR45sd4zP59OaNWu0ePFiTZ8+XZK0YcMG5eXlafPmzZo9e7YkqbKyUpL0hz/8ISZ9B5A8rMrLWGUlACQCO9SWAJAIqC0BIDJqSwCIDrUlAERGVgJAdMjL7sHMlgBMGhsbTUtzc3OXzldbWyun02kMtJSkiRMnyul0aseOHSGPOXLkiDwej0pLS41t6enpmjx5cofHAAAAAAAAAAAAAAAAAECsMNgSsLMY/BzPkCFD5HQ6jWX58uVd6qLH41Fubm677bm5ufJ4PB0eI0l5eXmm7Xl5eR0eAwBhMWU6AEQWg9oSAJISWQkAkVFbAkB0yEoAiIysBIDokJfdgp8RB2zM4bu8WHUuSaqvr1d2draxPT09PWR7t9utpUuXhj3nnj17Lp/b4Wi3z+fzhdxu6lPQ/miOAYBQrMpLqzIXABJRLGpLAEhG1JYAEBm1JQBEh9oSACIjKwEgOuRl92CwJQCT7Oxs02DLjsydO1czZswI26agoED79+/XiRMn2u07depUu5kr2+Tn50u6PMPloEGDjO0nT57s8BgAAAAAAAAAAAAAAAAAiBUGWwJ2ZuX0vVd4npycHOXk5ERsV1xcLK/Xq927d2vChAmSpF27dsnr9WrSpEkhjxk2bJjy8/NVU1OjcePGSZJaWlq0fft2rVix4so6CgCSdXnJt3gAJLM41pYAYCvUlgAQGbUlAESH2hIAIiMrASA65GW3YLAlYGN2+Dme0aNHq6ysTBUVFXr22WclSbNmzdLUqVM1cuRIo92oUaO0fPly3XvvvXI4HKqsrNSyZctUWFiowsJCLVu2TJmZmSovLzeO8Xg88ng8+vDDDyVJBw4cUFZWloYOHaoBAwbE5oIA2BJTpgNAZHaoLQEgEVBbAkBk1JYAEB1qSwCIjKwEgOiQl90jJd4dQA/hsGCBbW3atEk33HCDSktLVVpaqhtvvFG//e1vTW3q6urk9XqNxwsWLFBlZaXmzJmjW2+9VZ999pm2bdumrKwso80zzzyjcePGqaKiQpL01a9+VePGjdOrr77aPRcGAECi8wUtAAAAAABDQ0ODXC6XnE6nnE6nXC6Xzpw5E/YYn88nt9utwYMHq0+fPiopKdGhQ4eM/adPn9ajjz6qkSNHKjMzU0OHDtW8efNM9z4BBOGzIAAAAHQ3Pj9DJzGzJWBnNvk5ngEDBmjjxo3hn95n7oDD4ZDb7Zbb7e7wmEj7AcDAlOkAEJlNaksAiDtqSwCIzCa1ZXl5uY4eParq6mpJl3+Rx+Vy6bXXXuvwmJUrV2r16tVav369rrvuOj3xxBOaMmWK6urqlJWVpWPHjunYsWNatWqVxowZo08++USPPPKIjh07ppdeeil2FwPAnqgtASAyshIAokNedgsGWwIAAAAAAAAAgB7l8OHDqq6u1s6dO1VUVCRJWrdunYqLi1VXV6eRI0e2O8bn82nNmjVavHixpk+fLknasGGD8vLytHnzZs2ePVtjx47Vyy+/bBwzfPhwPfnkk/rud7+rixcvKi2Nj2UAAAAAALArfkYcsDGHz9oFAJIVWQkAkVFbAkB0yEoAiCwWtWVjY6NpaW5u7lIfa2tr5XQ6jYGWkjRx4kQ5nU7t2LEj5DFHjhyRx+NRaWmpsS09PV2TJ0/u8BhJ8nq9ys7OZqAlgHaoLQEgMrISAKJDXnYPBlsCduazeAGAZEVWAkBk1JYAEB2yEgAii0FtOWTIEDmdTmNZvnx5l7ro8XiUm5vbbntubq48Hk+Hx0hSXl6eaXteXl6Hx3z++ef62c9+ptmzZ3epvwCSFLUlAERGVgJAdMjLbsHXKAEAAAAAAAAAQEKrr69Xdna28Tg9PT1kO7fbraVLl4Y91549eyRJDoej3T6fzxdye6Dg/R0d09jYqG984xsaM2aMlixZEvacAAAAAAAg8TGzJWBzTAEMANEhKwEgMmpLAIgOWQkAkVldW2ZnZ5uWjgZbzp07V4cPHw67jB07Vvn5+Tpx4kS740+dOtVu5so2+fn5ktRuFsuTJ0+2O+bs2bMqKyvTVVddpa1bt6pXr15X8s8HoAehtgSAyOyQlQ0NDXK5XMZM7C6XS2fOnAl7jM/nk9vt1uDBg9WnTx+VlJTo0KFDHba955575HA49Morr1h/AQCSgh3y0u4YbAnYmc9n7QIAyYqsBIDIbFJbxuqm5XPPPaeSkhJlZ2fL4XCEPGdnnhtAErJBVgJA3MWxtszJydGoUaPCLhkZGSouLpbX69Xu3buNY3ft2iWv16tJkyaFPPewYcOUn5+vmpoaY1tLS4u2b99uOqaxsVGlpaXq3bu3Xn31VWVkZFzhPyCAHoPaEgAis0lWlpeXa9++faqurlZ1dbX27dsnl8sV9piVK1dq9erVqqqq0p49e5Sfn68pU6bo7Nmz7dquWbMm4gzsAHo4m+Sl3THYEgAAIAHEavCQx+ORy+VSfn6++vbtq1tuuUUvvfRSDK8ECc3XwQLYSKxuWp47d05lZWX68Y9/bOlzAwAAIDGNHj1aZWVlqqio0M6dO7Vz505VVFRo6tSpGjlypNFu1KhR2rp1qyTJ4XCosrJSy5Yt09atW3Xw4EHNnDlTmZmZKi8vl3R5RsvS0lJ9+eWXeuGFF9TY2CiPxyOPx6NLly7F5VqBDjnCLHZ+LgAAutnhw4dVXV2t559/XsXFxSouLta6dev0+uuvq66uLuQxPp9Pa9as0eLFizV9+nSNHTtWGzZs0Llz57R582ZT2/fff1+rV6/Wr3/96+64HCA58dkYLJIW7w4A6Dwrp/BlKmAAycyqvIxlVpaXl+vo0aOqrq6WJM2aNUsul0uvvfZah8e0DR5av369rrvuOj3xxBOaMmWK6urqlJWVJUlyuVzyer169dVXlZOTo82bN+vBBx/U3r17NW7cuNhdEADbsUNt2XbTcufOnSoqKpIkrVu3TsXFxaqrqzN9KN4m+KalJG3YsEF5eXnavHmzZs+eLUmqrKyUJP3hD3+w7LkBJCc71JYAEG92qC0ladOmTZo3b55KS0slSdOmTVNVVZWpTV1dnbxer/F4wYIFampq0pw5c9TQ0KCioiJt27bNeB/+zjvvaNeuXZKkESNGmM515MgRFRQUxO6CANgOtSUARGZ1VjY2Npq2p6enKz09vUvnrq2tldPpNO4bStLEiRPldDq1Y8eOkPcOjxw5Io/HY9SibX2ZPHmyduzYYdy3PHfunP7xH/9RVVVVys/P71I/ASQ3asvuwcyWAAAAcRbLbzzW1tbq0Ucf1YQJE3Tttdfq8ccfV79+/fTuu+921+UB6MEaGxtNS3Nzc5fOF+mmZSiRblrG8rkBAACQ2AYMGKCNGzca9erGjRvVr18/Uxufz6eZM2cajx0Oh9xut44fP67z589r+/btGjt2rLG/pKREPp8v5MJASwAAgPgbMmSI8StjTqdTy5cv7/I5PR6PcnNz223Pzc2Vx+Pp8BhJysvLM23Py8szHTN//nxNmjRJ3/rWt7rcTwBA1zHYErCzjn4KtLMLACSrBM/KWA4euu2227RlyxadPn1ara2tevHFF9Xc3KySkpLYXAwA+4pBbWn1jctY3rSMxXMDSFIJXltKUkNDg1wul5G/LpdLZ86cCXuMz+eT2+3W4MGD1adPH5WUlOjQoUMdtr3nnnvkcDj0yiuvWH8BAOyP+5YAEB2yEgAiszgr6+vr5fV6jWXRokUdPrXb7ZbD4Qi77N27V9LlL+W067rPF3J7oOD9gce8+uqreuutt7RmzZqw5wAASdSW3YSfEQdszNF6ebHqXACQrKzKy7ZzWP0TE1YPHvrkk0+Mx1u2bNGDDz6ogQMHKi0tTZmZmdq6dauGDx/e6f4CSE6xqC3r6+uVnZ1tbO8oK91ut5YuXRr2nHv27Ll87hjctIxWZ58bQHKxuraMhfLych09elTV1dWSpFmzZsnlcum1117r8JiVK1dq9erVWr9+va677jo98cQTmjJliurq6oyfxm2zZs0asg9AWNy3BIDo2KG2BIB4szors7OzTfcsw5k7d65mzJgRtk1BQYH279+vEydOtNt36tSpdp/jtGn7SXCPx6NBgwYZ20+ePGkc89Zbb+mjjz5qN/v6fffdp9tvv11/+MMforoOAD0DtWX3YGZLAACAKxTtTG3x/sajJD3++ONqaGjQm2++qb179+qxxx7T/fffrwMHDlzpZQPAFWu7cdm2dDTYcu7cuTp8+HDYZezYscrPz+/STctAgTcto9GZ5waAeDh8+LCqq6v1/PPPq7i4WMXFxVq3bp1ef/111dXVhTzG5/NpzZo1Wrx4saZPn66xY8dqw4YNOnfunDZv3mxq+/7772v16tX69a9/3R2XAwAAgDhj1nQAPVlOTo5GjRoVdsnIyFBxcbG8Xq92795tHLtr1y55vV5NmjQp5LmHDRum/Px81dTUGNtaWlq0fft245iFCxdq//792rdvn7FI0tNPP63f/OY3sbtwAECHmNkSsDMrp+9lGmAAycyqvAz4iYloZmqL9zceP/roI1VVVengwYO6/vrrJUk33XST/vjHP+qXv/ylnnnmmbB9A9DDxLG2zMnJUU5OTsR2gTctJ0yYIOnKblqOGzdOkv+m5YoVK6LuY2eeG0CSsri2tHrW9NraWjmdThUVFRnbJk6cKKfTqR07dmjkyJHtjjly5Ig8Ho9KS0tN/Zg8ebJ27Nih2bNnS5LOnTunf/zHf1RVVZVRjwJASNy3BIDoWFxbxgKzpgOIOxtk5ejRo1VWVqaKigo9++yzki7n5dSpU03vw0eNGqXly5fr3nvvlcPhUGVlpZYtW6bCwkIVFhZq2bJlyszMVHl5uaTLnwWFev89dOhQDRs2LHYXBMCebJCXyYDBloCNOXyXF6vOBQDJyqq8bDtHtD8xEe/BQ+fOnZMkpaSYJzNPTU1VayvzvwMws0NtGaubltLlwesej0cffvihJOnAgQPKysrS0KFDNWDAgKifG0Dys7q2HDJkiGn7kiVL5Ha7O31ej8ej3Nzcdttzc3PbzfIbeIykdl/0ycvL0yeffGI8nj9/viZNmqRvfetbne4fgJ7BDrUlACQCq2tLq7XNmr5z507jyzzr1q1TcXGx6urqQr4fDp41XZI2bNigvLw8bd682fgij+SfNX3Pnj2mL5QDQKBEz8o2mzZt0rx584wvMk6bNk1VVVWmNnV1dfJ6vcbjBQsWqKmpSXPmzFFDQ4OKioq0bdu2dgPTASAadslLu2OwJQAAQJzFavDQqFGjNGLECM2ePVurVq3SwIED9corr6impkavv/56XK4VCSrcmyarJxbgDRq6KFY3LZ955hktXbrUePzVr35VkvSb3/xGM2fOjPq5AeBKRTtrutvtNuVUKHv27JGkkDMD+Xy+iDMGBe8PPObVV1/VW2+9pffeey/sOQAAQJJgokGIWdMB4EoMGDBAGzduDNvG5zPfIHc4HHK73Vf0pcvgcwAIwksEMcZgS8DOfL7Li1XnAoBkZVVexjArYzF4qFevXnrjjTe0cOFCffOb39QXX3yhESNGaMOGDfr6178es2sBYFM2qS1jddMympua0Tw3gB7A4toy2lnT586dqxkzZoRtU1BQoP379+vEiRPt9p06dardzJVt2j7c9ng8phmFTp48aRzz1ltv6aOPPlK/fv1Mx9533326/fbb9Yc//CHiNQDoQWxSWwJA3FlcWzY2Npo2p6end/hlnmgwazqAhGCDz3gAICGQl92CwZYAAAAJIFaDhwoLC/Xyyy9b0UUAAADEUU5OjnJyciK2Ky4ultfr1e7duzVhwgRJ0q5du+T1ejVp0qSQxwwbNkz5+fmqqanRuHHjJEktLS3avn27VqxYIUlauHChHn74YdNxN9xwg55++ml985vf7MqlAQAAwCJDhgwxPV6yZEnIe4fMmg4AAAB0DoMtARtz+C4vVp0LAJKVVXlJVgJIZtSWABCdRK8tR48erbKyMlVUVOjZZ5+VJM2aNUtTp041/czjqFGjtHz5ct17771yOByqrKzUsmXLVFhYqMLCQi1btkyZmZkqLy+XdHn2y1A/7zh06FANGzYsNhcDwLaoLQEgOlbXlvX19aZZ0zua1ZJZ0wHYSaK/DweAREFedg8GWwJ25vvbYtW5ACBZWZWXZCWAZEZtCQDRsUFtuWnTJs2bN0+lpaWSpGnTpqmqqsrUpq6uTl6v13i8YMECNTU1ac6cOWpoaFBRUZG2bdumrKys2HUUQPKitgSA6FhcW2ZnZ5sGW3aEWdMB2IoN3ocDQEIgL7sFgy0BAAAAAACAJDJgwABt3LgxbBufz3zX1OFwyO12h/yZyWjPAQAAgOTCrOkAAACAGYMtARvj53gAIDpMmQ4AkVFbAkB0qC0BIDJqSwCIjh1qS2ZNBxBvdshKAEgE5GX3YLAlYGc+3+XFqnMBQLKyKi/JSgDJjNoSAKJDbQkAkVFbAkB0bFBbMms6gLizQVYCQEIgL7sFgy0BAAAAdIz3UwAAAAAAAADiwRGDc3bX/U479x1A8og2i6zIFzIKPQSDLQEb4+d4ACA6TJkOAJFRWwJAdKgtASAyaksAiA61JQBERlYCQHTIy+7BYEvAznyy7tsBhCWAZGZVXpKVAJIZtSUARIfaEgAio7YEgOhQWwJAZGQlAESHvOwWKfHuAAAAAAAAAAAAAAAAAAAAQCKz3WDL5uZm3XzzzXI4HNq3b1+8uwPEVdsUwFYtSC7kJeBHVqIjZCXgR22JjpCVgBlZiY6Ql4AftSU6QlYCZmQlOkJeAn5kJTpCVgJm5GX3sN1gywULFmjw4MHx7gYAJDzyEgAiIysBIDKyEgCiQ14CQGRkJQBEh7wEgMjISgDxYKvBlv/5n/+pbdu2adWqVfHuCpAYWn3WLkga5CUQhKxECGQlEITaEiGQlUAIZCVCIC+BINSWCIGsBEIgKxECeQkEISsRAlkJhEBedou0eHcgWidOnFBFRYVeeeUVZWZmRnVMc3OzmpubjceNjY2x6h4QH76/LVadC0nhSvOSrESPYFVekpVJg9oSCIHaEkHISqAD1JYIQl4CIVBbIghZCXSA2hJByEsgBLISQchKoAPkZbewxcyWPp9PM2fO1COPPKJbb7016uOWL18up9NpLEOGDIlhLwEg/jqTl2QlgJ6G2hIAIiMro+CzeOlp/QOSBHkJAJGRlQAQHfIyBKvf23bn+1s79x1IYGTlFUrEfHFYsABxFNfBlm63Ww6HI+yyd+9erV27Vo2NjVq0aNEVnX/RokXyer3GUl9fH6MrAeLDIcnhs2iJ98UgrFjmJVmJnsCyvIz3hSAsakuga6gtewayEug6asuegbwEuobasmcgK4Guo7bsGchLoGvIyp6BrAS6jrzsHnH9GfG5c+dqxowZYdsUFBToiSee0M6dO5Wenm7ad+utt+qf/umftGHDhpDHpqentzsGSCo+3+XFqnMhYcUyL8lK9AhW5SVZmdCoLYEuorbsEchKwALUlj0CeQl0EbVlj0BWAhagtuwRyEugi8jKHoGsBCxAXnaLuA62zMnJUU5OTsR2v/jFL/TEE08Yj48dO6a7775bW7ZsUVFRUSy7CAAJgbwEgMjISgCIjKwEgOiQlwAQGVkJANEhLwEgMrISgF3EdbBltIYOHWp6fNVVV0mShg8frquvvjoeXQISQtsUvladC/ZHXgKhWZWXZGVyICuB0KgtEYisBDpGbYlA5CUQGrUlApGVQMeoLRGIvARCIysRiKwEOkZedo+UeHcAAAAAAAAAAAAAAAAAAAAgkdlysGVBQYF8Pp9uvvnmeHcFiC+fxQuSDnkJ/A1ZiTDISuBvqC0RBlkJBCArEQZ5CfwNtSXCICuBAGQlwiAvgb8hKxEGWQkEsEFeNjQ0yOVyyel0yul0yuVy6cyZM2GP8fl8crvdGjx4sPr06aOSkhIdOnTI1Ka5uVmPPvqocnJy1LdvX02bNk1Hjx4Neb7m5mbdfPPNcjgc2rdv3xVfgy0HWwK4zOHzWboAQLIiKwEgMmpLAIgOWQkAkVFbAkB0yEoAiIysBIDo2CEvy8vLtW/fPlVXV6u6ulr79u2Ty+UKe8zKlSu1evVqVVVVac+ePcrPz9eUKVN09uxZo01lZaW2bt2qF198UW+//ba++OILTZ06VZcuXWp3vgULFmjw4MGdvgYGWwIAAAAAAAAAAAAAAAAAgJg4fPiwqqur9fzzz6u4uFjFxcVat26dXn/9ddXV1YU8xufzac2aNVq8eLGmT5+usWPHasOGDTp37pw2b94sSfJ6vXrhhRf01FNP6a677tK4ceO0ceNGHThwQG+++abpfP/5n/+pbdu2adWqVZ2+DgZbAnbWavECAMmKrASAyKgtgSvjsHjpaf2zM7ISACKjtgSA6JCVQHhWv7e14n1wIvYp2ZGVQOclYvYk8E9c257FednY2Ghampubu9S92tpaOZ1OFRUVGdsmTpwop9OpHTt2hDzmyJEj8ng8Ki0tNbalp6dr8uTJxjHvvPOOLly4YGozePBgjR071nTeEydOqKKiQr/97W+VmZnZ6etI6/SRAOLOyul7mTYdQDKzKi/JSgDJjNoSAKJDbQkAkVFbAkB0qC0BIDKyEgCiY3VeDhkyxLR9yZIlcrvdnT6vx+NRbm5uu+25ubnyeDwdHiNJeXl5pu15eXn65JNPjDa9e/dW//7927VpO97n82nmzJl65JFHdOutt+rjjz/u9HUw2BIAAAAAAAAAAAAAAAAAAEiS6uvrlZ2dbTxOT08P2c7tdmvp0qVhz7Vnzx5JksPRfrpUn88Xcnug4P3RHBPYZu3atWpsbNSiRYvCHhMNBlsCdmblFMl8kQdAMrMqL8lKAMmM2hIAokNtCQCRUVsCQHSoLQEgMrISAKJjcV5mZ2ebBlt2ZO7cuZoxY0bYNgUFBdq/f79OnDjRbt+pU6fazVzZJj8/X9Ll2SsHDRpkbD958qRxTH5+vlpaWtTQ0GCa3fLkyZOaNGmSJOmtt97Szp072w0YvfXWW/VP//RP2rBhQ8TrbMNgSwAAAAAAAAAAAAAAAAAAcEVycnKUk5MTsV1xcbG8Xq92796tCRMmSJJ27dolr9drDIoMNmzYMOXn56umpkbjxo2TJLW0tGj79u1asWKFJGn8+PHq1auXampq9MADD0iSjh8/roMHD2rlypWSpF/84hd64oknjPMeO3ZMd999t7Zs2aKioqIrul4GWwJ25vNdXqw6FwAkK6vykqwEkMyoLQEgOtSWABAZtSUARIfaEgAiIysBIDoJnpejR49WWVmZKioq9Oyzz0qSZs2apalTp2rkyJFGu1GjRmn58uW699575XA4VFlZqWXLlqmwsFCFhYVatmyZMjMzVV5eLklyOp166KGH9IMf/EADBw7UgAED9MMf/lA33HCD7rrrLknS0KFDTX256qqrJEnDhw/X1VdffUXXwWBLwMYcvsuLVecCgGRlVV6SlQCSGbUlAESH2hIAIqO2BIDoUFsCQGRkJQBExw55uWnTJs2bN0+lpaWSpGnTpqmqqsrUpq6uTl6v13i8YMECNTU1ac6cOWpoaFBRUZG2bdumrKwso83TTz+ttLQ0PfDAA2pqatKdd96p9evXKzU11fJrYLAlAAAAAAAAAAAAAAAAAACImQEDBmjjxo1h2/iCZtZ0OBxyu91yu90dHpORkaG1a9dq7dq1UfWjoKCg3fNEi8GWgJ3xczwAEJ0EnzIdABICtSVwZaz+M3dYfL5E75+dUVsCQGTUlgAQHWpLILxE/NNOxD4lO7IS6LxE/LO34j5jIl5XIiAvuwWDLQEbc7ReXqw6FwAkK6vykqwEkMyoLQEgOtSWABAZtSUARIfaEgAiIysBIDrkZfdIiXcHAAAAAAAAAAAAAAAAAAAAEhmDLQE7a5sC2KoFAJIVWQkAkVFbAkB0yEoAiIzaEgCiQ1YCQGQ2ycqGhga5XC45nU45nU65XC6dOXMmwqX55Ha7NXjwYPXp00clJSU6dOhQu3a1tbW644471LdvX/Xr108lJSVqamqK0ZUAsC2b5KXdMdgSsDOfxQsAJCuyEgAis0ltGaubls8995xKSkqUnZ0th8MR8pwFBQVyOBymZeHChRZeHQBbsEFWAkDc2aS2BIC4IysBIDKbZGV5ebn27dun6upqVVdXa9++fXK5XGGPWblypVavXq2qqirt2bNH+fn5mjJlis6ePWu0qa2tVVlZmUpLS7V7927t2bNHc+fOVUoKw30ABLFJXtpdWrw7AAAAAABAtMrLy3X06FFVV1dLkmbNmiWXy6XXXnutw2PablquX79e1113nZ544glNmTJFdXV1ysrKkiSdO3dOZWVlKisr06JFizo8109/+lNVVFQYj6+66iqLrgwAAAAAAACAHR0+fFjV1dXauXOnioqKJEnr1q1TcXGx6urqNHLkyHbH+Hw+rVmzRosXL9b06dMlSRs2bFBeXp42b96s2bNnS5Lmz5+vefPmmb70XVhY2A1XBQAIhcGWgI05fD45LJq+16rzAEAisiovyUoAycwOtWUsb1pWVlZKkv7whz+E7UNWVpby8/OtuygAtkNtCQCR2aG2BIBEQG0JAJFZnZWNjY2m7enp6UpPT+/SuWtra+V0Oo17lpI0ceJEOZ1O7dixI+R9yyNHjsjj8ai0tNTUl8mTJ2vHjh2aPXu2Tp48qV27dumf/umfNGnSJH300UcaNWqUnnzySd12221d6jOA5ENt2T2YVxgAAAAAEBONjY2mpbm5uUvni3TTMpRINy2v1IoVKzRw4EDdfPPNevLJJ9XS0nLlFwIAAAAAAAAgLoYMGSKn02ksy5cv7/I5PR6PcnNz223Pzc2Vx+Pp8BhJysvLM23Py8sz9v3lL3+RJLndblVUVKi6ulq33HKL7rzzTv35z3/ucr8BAFeOmS0BO/P5Li9WnQsAkpVVeUlWAkhmMagthwwZYtq8ZMkSud3uTp/W6puWn3zyyRU9//e//33dcsst6t+/v3bv3q1FixbpyJEjev7556/oPEgSjnh3IIJE75+dUVsCQGTctwSA6FBbAuHF871tRy+rROxTsrM4K+vr65WdnW1sDjerpdvt1tKlS8Oeds+ePZIkh6P9H4fP5wu5PVDw/sBjWltbJUmzZ8/W9773PUnSuHHj9F//9V/69a9/bclAUSQ5KzLL6uzpqVnWHagtuwWDLQE780lqtfBcAJCsrMpLshJAMotBbRntjct437SM1vz58431G2+8Uf3799d3vvMdY7ZLAD0EtSUARMZ9SwCIDrUlAERmcVZmZ2eb7lmGM3fuXM2YMSNsm4KCAu3fv18nTpxot+/UqVPtvgTeJj8/X9LlL4sPGjTI2H7y5EnjmLbtY8aMMR07evRoffrpp1FdA4AehNqyW/Az4gAAAACAmGi7cdm2dDTYcu7cuTp8+HDYZezYscrPz+/STctAgTctO2vixImSpA8//LBL5wEAqzU0NMjlchk/ieZyuXTmzJmwx/h8Prndbg0ePFh9+vRRSUmJDh061K5dbW2t7rjjDvXt21f9+vVTSUmJmpqaYnQlAAAAAADET05OjkaNGhV2ycjIUHFxsbxer3bv3m0cu2vXLnm9Xk2aNCnkuYcNG6b8/HzV1NQY21paWrR9+3bjmIKCAg0ePFh1dXWmY//0pz/pmmuuicEVAwAiYWZLwMYcPp8cFk3fa9V5ACARWZWXZCWAZBbP2jInJ0c5OTkR2wXetJwwYYKkK7tpOW7cOEn+m5YrVqy4on4Ge++99yTJ9M1zAMnPDrVleXm5jh49qurqaknSrFmz5HK59Nprr3V4zMqVK7V69WqtX79e1113nZ544glNmTJFdXV1ysrKknR5oGVZWZkWLVqktWvXqnfv3nr//feVksL3uQGYcd8SAKJjh9oSAOLNDlk5evRolZWVqaKiQs8++6yky+/Fp06dqpEjRxrtRo0apeXLl+vee++Vw+FQZWWlli1bpsLCQhUWFmrZsmXKzMxUeXn55T47HPrRj36kJUuW6KabbtLNN9+sDRs26IMPPtBLL70Us+sBYE92yMtkwGBLwM58kqwKObISQDKzKi/JSgDJzAa1ZaxuWkqXZ770eDzGLJUHDhxQVlaWhg4dqgEDBqi2tlY7d+7U1772NTmdTu3Zs0fz58/XtGnTNHTo0NhcMIDElOC15eHDh1VdXa2dO3eqqKhIkrRu3ToVFxerrq7OlJdGV3w+rVmzRosXL9b06dMlSRs2bFBeXp42b96s2bNnS5Lmz5+vefPmaeHChcaxhYWFsbkQAPZmg9oSABJCgteWAJAQbJKVmzZt0rx581RaWipJmjZtmqqqqkxt6urq5PV6jccLFixQU1OT5syZo4aGBhUVFWnbtm3Glx4lqbKyUufPn9f8+fN1+vRp3XTTTaqpqdHw4cNje0EA7McmeWl3fO0cAAAAAGAbmzZt0g033KDS0lKVlpbqxhtv1G9/+1tTm1A3LSsrKzVnzhzdeuut+uyzz9rdtHzmmWc0btw4VVRUSJK++tWvaty4cXr11VclSenp6dqyZYtKSko0ZswY/Y//8T9UUVGh3/3ud91w1QCSWWNjo2lpbm7u0vlqa2vldDqNgZaSNHHiRDmdTu3YsSPkMUeOHJHH4zE+EJIu597kyZONY06ePKldu3YpNzdXkyZNUl5eniZPnqy33367S/0FgHhqaGiQy+WS0+mU0+mUy+XSmTNnwh7j8/nkdrs1ePBg9enTRyUlJTp06FCHbe+55x45HA698sor1l8AAAAAEsaAAQO0ceNG4/39xo0b1a9fP1Mbn8+nmTNnGo8dDofcbreOHz+u8+fPa/v27Ro7dmy7cy9cuFD19fX68ssvtWPHDt12220xvhoAQEcYbAnYmc9n7QIAyYqsBIDIbFJbxuqmpdvtls/na7e0neeWW27Rzp07debMGTU1NemDDz6Q2+1WZmZmzK4VQIKyOCuHDBliDPJxOp1avnx5l7rn8XiUm5vbbntubq48Hk+Hx0hSXl6eaXteXp6x7y9/+Yuky3lZUVGh6upq3XLLLbrzzjv15z//uUt9BpCEbFJblpeXa9++faqurlZ1dbX27dsnl8sV9piVK1dq9erVqqqq0p49e5Sfn68pU6bo7Nmz7dquWbNGDocjVt0HkAxskJWxHJheW1urO+64Q3379lW/fv1UUlKipqamGF0JANuyQVYCQEIgL7sFgy0BAAAAAACAOKmvr5fX6zWWRYsWhWzndrvlcDjCLnv37pWkkAN7fD5fxAE/wfsDj2ltbZUkzZ49W9/73vc0btw4Pf300xo5cqR+/etfX/F1A0C8HT58WNXV1Xr++edVXFys4uJirVu3Tq+//rrq6upCHuPz+bRmzRotXrxY06dP19ixY7VhwwadO3dOmzdvNrV9//33tXr1ajISgO3FamB6bW2tysrKVFpaqt27d2vPnj2aO3euUlL4+BoAAACJKy3eHQDQBa2SrPpidKtF5wGARGRVXpKVAJIZtSVwZaz+cq/Vk14lev/szOLaMjs7W9nZ2RGbz507VzNmzAjbpqCgQPv379eJEyfa7Tt16lS7mSvb5OfnS7o8w+WgQYOM7SdPnjSOads+ZswY07GjR4/Wp59+GrH/AHqYGNSWjY2Nps3p6elKT0/v9Glra2vldDpVVFRkbJs4caKcTqd27NihkSNHtjvmyJEj8ng8Ki0tNfVj8uTJ2rFjh2bPni1JOnfunP7xH/9RVVVVRsYCQEgJft+ybWD6zp07jbxct26diouLVVdXFzIrgwemS9KGDRuUl5enzZs3G1k5f/58zZs3TwsXLjSOLSwsjM2FwL4ScWKtROxTskvwrAQSWqJnVmdf24l+XfFCXnYLvhoE2JjD57N0AYBkRVYCQGTUlgAQnXhlZU5OjkaNGhV2ycjIUHFxsbxer3bv3m0cu2vXLnm9Xk2aNCnkuYcNG6b8/HzV1NQY21paWrR9+3bjmIKCAg0ePLjdbG9/+tOfdM0111zRtQBIfrGoLYcMGWL8hK3T6dTy5cu71EePx6Pc3Nx223Nzc+XxeDo8RlK7wet5eXmmY+bPn69JkybpW9/6Vpf6CCD5WZ2VjY2NpqW5ublL/Ys0MD2USAPTpctf6tm1a5dyc3M1adIk5eXlafLkyXr77be71F8AyYl7lgAQHfKyezDYEgAAAAAAAEgSo0ePVllZmSoqKrRz507t3LlTFRUVmjp1qmnmoVGjRmnr1q2SLv98eGVlpZYtW6atW7fq4MGDmjlzpjIzM1VeXm60+dGPfqRf/OIXeumll/Thhx/qJz/5iT744AM99NBDcblWAD1LfX29vF6vsSxatChkO7fbLYfDEXbZu3evpMvZFszn84XcHih4f+Axr776qt566y2tWbOmE1cJAF1jl4Hpf/nLXyRdzuyKigpVV1frlltu0Z133qk///nPXeozAAAAEEv8jDhgZz7f5cWqc8VIQ0OD5s2bp1dffVWSNG3aNK1du1b9+vUL0x2fli5dqueee04NDQ0qKirSL3/5S11//fWSpNOnT2vJkiXatm2b6uvrlZOTo29/+9v62c9+JqfTGbNrAWBTVuUl3+IBkMxsUlsCQNzZoLbctGmT5s2bZ8wmNG3aNFVVVZna1NXVyev1Go8XLFigpqYmzZkzx3gfvm3bNmVlZRltKisrdf7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      "text/plain": [
       "<Figure size 2666.67x500 with 16 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_states = 8\n",
    "\n",
    "states_plot = states.real\n",
    "#states_plot = np.angle(states)\n",
    "#states_plot = states.imag\n",
    "#states_plot = np.abs(states)**2\n",
    "\n",
    "# Create a 1xn_states grid of subplots (1 row, n_states columns)\n",
    "fig, axes = plt.subplots(1, n_states, figsize=(20/6*n_states, 5))  # Adjust the size as needed\n",
    "\n",
    "# Loop over the state numbers from 0 to n_states-1\n",
    "for state_number, ax in zip(range(n_states), axes):\n",
    "    # Slice through the y-direction and rotate the x-z plane (by swapping x and z)\n",
    "    im = ax.imshow(states_plot[state_number, :, int(len(y)/2), :].T,\n",
    "                   extent=[*extend[0], *extend[2]], origin=\"lower\",\n",
    "                   vmin=np.min(states_plot[state_number]), vmax=np.max(states_plot[state_number]))\n",
    "\n",
    "    # Set labels for each subplot\n",
    "    ax.set_xlabel(\"x\")\n",
    "    ax.set_ylabel(\"z\")\n",
    "    ax.set_title(f\"State {state_number}\")\n",
    "    fig.colorbar(im, ax=ax)  \n",
    "\n",
    "# Adjust layout for better spacing\n",
    "plt.tight_layout()\n",
    "\n",
    "# Show the plots\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(energies,\"o\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Normalise the states to give 1 over 3D integral:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "states /= np.sqrt(np.prod(dvol))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0000121523186054"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#check if normalisation is correct\n",
    "\n",
    "integrand  = np.abs(states[0])**2\n",
    "\n",
    "integral_z = simpson(integrand, dx=dvol[2], axis=2)\n",
    "integral_y = simpson(integral_z, dx=dvol[1], axis=1)\n",
    "total_integral = simpson(integral_y, dx=dvol[0], axis=0)\n",
    "\n",
    "total_integral"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0000000000000013"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#just suming gives almost the same result\n",
    "np.sum(integrand)*np.prod(dvol)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Find wavefunctions that are localised in each well"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "state_number = 0\n",
    "phase_mult0 = np.exp(-1.91*1j)\n",
    "\n",
    "plt.plot(x,(phase_mult0*states[state_number,:,int(len(y)/2),int(len(z)/2)]).real, label=\"real part\")\n",
    "plt.plot(x,(phase_mult0*states[state_number,:,int(len(y)/2),int(len(z)/2)]).imag, label=\"imaginary part\")\n",
    "#plt.plot(x,pot[:,int(len(y)/2),int(len(z)/2)], label=\"potential (rescaled)\")\n",
    "plt.legend()\n",
    "plt.show()\n",
    "\n",
    "state_number = 1\n",
    "phase_mult1 = np.exp((-0.791)*1j)\n",
    "\n",
    "plt.plot(x,(phase_mult1*states[state_number,:,int(len(y)/2),int(len(z)/2)]).real, label=\"real part\")\n",
    "plt.plot(x,(phase_mult1*states[state_number,:,int(len(y)/2),int(len(z)/2)]).imag, label=\"imaginary part\")\n",
    "#plt.plot(x,pot[:,int(len(y)/2),int(len(z)/2)], label=\"potential (rescaled)\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "theta = np.deg2rad(45)\n",
    "\n",
    "GS_left = (np.cos(theta)*states[0] + np.sin(theta)*states[1])\n",
    "GS_left /= np.sqrt(np.sum(np.abs(GS_left)**2)*np.prod(dvol))\n",
    "\n",
    "GS_right = (np.sin(theta)*states[0] - np.cos(theta)*states[1])\n",
    "GS_right /= np.sqrt(np.sum(np.abs(GS_right)**2)*np.prod(dvol))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "GS_left = (phase_mult0*states[0] - phase_mult1*states[1])\n",
    "GS_left /= np.sqrt(np.sum(np.abs(GS_left)**2)*np.prod(dvol))\n",
    "\n",
    "GS_right = (phase_mult0*states[0] + phase_mult1*states[1])\n",
    "GS_right /= np.sqrt(np.sum(np.abs(GS_right)**2)*np.prod(dvol))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [],
   "source": [
    "state_S = states[1].real\n",
    "state_S /= np.sqrt(np.sum(np.abs(state_S)**2)*np.prod(dvol))\n",
    "\n",
    "state_A = states[0].real\n",
    "state_A /= np.sqrt(np.sum(np.abs(state_A)**2)*np.prod(dvol))\n",
    "\n",
    "\n",
    "GS_left = (state_S - state_A)\n",
    "GS_left /= np.sqrt(2)#np.sqrt(np.sum(np.abs(GS_left)**2)*np.prod(dvol))\n",
    "\n",
    "GS_right = (state_S + state_A)/np.sqrt(2)\n",
    "GS_right /= np.sqrt(2)#np.sqrt(np.sum(np.abs(GS_right)**2)*np.prod(dvol))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [],
   "source": [
    "test = np.reshape(functional_hamiltonian(dvol, pot, mass)(np.reshape(states[1], -1)),size)/energies[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [],
   "source": [
    "test = np.reshape(ham @ np.reshape(states[1], -1),size)/energies[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x,(states[1]-test)[:,int(len(y)/2),int(len(z)/2)].real, label=\"real part\")\n",
    "plt.plot(x,(states[1])[:,int(len(y)/2),int(len(z)/2)].real, label=\"imaginary part\")\n",
    "#plt.plot(x,pot[:,int(len(y)/2),int(len(z)/2)], label=\"potential (rescaled)\")\n",
    "plt.legend()\n",
    "plt.show()\n",
    "\n",
    "plt.plot(x,state_S[:,int(len(y)/2),int(len(z)/2)].real, label=\"real part\")\n",
    "plt.plot(x,state_S[:,int(len(y)/2),int(len(z)/2)].imag, label=\"imaginary part\")\n",
    "#plt.plot(x,pot[:,int(len(y)/2),int(len(z)/2)], label=\"potential (rescaled)\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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7uRqgewgvANDKveIohEdezJ11GXVBMCO8AEArK2xU17ZMmvCC4EV4AYBWVpg2alsmTbMughfhBQBamdNGFXVNqm1o9nM13ud0Gdr5NdNGCH6EFwBoFR8VoT5RLU2soTj68p+yWtU3ueQID9OAlFh/lwN0G+EFAI7RNylGUmg27e48ZnM6exjHAiB4EV4A4Bjm1NFXITjy4t5ZN4MpIwQ3wgsAHKNfCJ8u7d5Zl2ZdBDnCCwAcwz3yUh56RwR83jrywjJpBDvCCwAcI1SXS9c2NKvoSEsgY6URgh3hBQCOEaq77JpLpNPiHUppPT0bCFaEFwA4hjnyUlrdoIZmp5+r8R7zWIChjLogBBBeAOAYKbGRiopo+aexuKLez9V4z07zWACadRECCC8AcAybzdY2dRRCfS8sk0YoIbwAwHFCbaM6wzCOWSZNeEHwI7wAwHFCbaO64sp6VdU3yx5m06D0OH+XA/QY4QUAjhNqG9WZxwIMTIuVI9zu52qAniO8AMBx2npeQmOjuoOVLSHslGQOY0RoILwAwHFCbaO6IzWNklpWUgGhgPACAMcxR16KK+rldBl+rqbnympbwktyHOEFoYHwAgDHyegTpfAwm5pdhkqrg3+vlyO1jLwgtBBeAOA49jCbMhOiJElfhUDTrhlekmIILwgNhBcA6EAonXHEtBFCDeEFADoQSk27R2obJDFthNBBeAGADvQzN6oL8pEXwzDc00bJhBeECJ+Gl/Lyck2bNk0JCQlKSEjQtGnTVFFR0elzZs6cKZvN1u523nnn+bJMADhBqIy8VDc0q8nZsmIqJdbh52oA7wj35YtfeeWV+uqrr/Tuu+9Kkn7+859r2rRp+sc//tHp8yZMmKDFixe7P46M5LcFAL2rn/t8o+DeqM7c4yU6wq7oSHbXRWjwWXjZsWOH3n33Xa1du1ajRo2SJD377LMqKCjQzp07NWTIkG98rsPhUGZmpq9KA4CTOvZkacMwZLPZ/FxR95QxZYQQ5LNpozVr1ighIcEdXCTpvPPOU0JCgj755JNOn7ty5Uqlp6dr8ODBmjVrlkpLS7/xsQ0NDaqqqmp3A4CeykpsWSpd3+Ry94wEI/ceL6w0QgjxWXgpKSlRenr6Cfenp6erpKTkG5938cUXa+nSpfrggw+0aNEirV+/Xt/5znfU0NDQ4eMXLlzo7qlJSEhQTk6O174GANblCLcrPb6lRySY+17MlUaMvCCUeBxe5s+ff0JD7fG3DRs2SFKHw6wnG369/PLL9f3vf195eXmaNGmS3nnnHe3atUtvvfVWh4+/7bbbVFlZ6b7t37/f0y8JADrUNwROlz5S2ySJ8ILQ4nHPy5w5c3TFFVd0+pgBAwZoy5Yt+vrrr0/43KFDh5SRkdHl62VlZal///764osvOvy8w+GQw0EHPQDv65sYrU1FFSEx8sIeLwglHoeX1NRUpaamnvRxBQUFqqys1Lp163TuuedKkv71r3+psrJSo0eP7vL1ysrKtH//fmVlZXlaKgD0iDnyEsx7vbQ17PJLHkKHz3pehg0bpgkTJmjWrFlau3at1q5dq1mzZumSSy5pt9Jo6NChWrZsmSSppqZGt9xyi9asWaN9+/Zp5cqVmjRpklJTU3XppZf6qlQA6FC/xODf64VDGRGKfLpJ3dKlS5Wfn69x48Zp3LhxOuOMM/TCCy+0e8zOnTtVWVkpSbLb7dq6dasmT56swYMHa8aMGRo8eLDWrFmj+Ph4X5YKACcIhZEXdtdFKPLpJnXJycn63//9304fYxiG+8/R0dF67733fFkSAHRZ38Tg36iurIZDGRF6ONsIAL6BOfJSVd+s6vomP1fTPUwbIRQRXgDgG8Q5wpUQHSEpOPtejjY6dbTJKYlpI4QWwgsAdKJfEO/1Uta6TDrSHqY4h0+7BIBeRXgBgE70DeIVR+aUUVJsRNCezQR0hPACAJ0I5l122eMFoYrwAgCdMEdevgrGkZcamnURmggvANCJYO55YY8XhCrCCwB0wr3XSxCOvJQRXhCiCC8A0Amz5+VQdYPqW5cdBwsOZUSoIrwAQCeSYiIUHWGXJBVX1vu5Gs+4p43YXRchhvACAJ2w2WxBu+KojN11EaIILwBwEu4VR0F2xtERlkojRBFeAOAk3CMvQda0y2ojhCrCCwCchHuX3SCaNmpsdqm6vlkS00YIPYQXADgJc6+XYNqorryuZdTFHmZzHy4JhArCCwCcRDBuVFfWurtuUkyEwsI41wihhfACACdhblRXUlWvZqfLz9V0Df0uCGWEFwA4ifR4hyLsNjldhr6ubvB3OV1S1rpBHeEFoYjwAgAnERZmU1ZCcE0dHXHv8cIyaYQewgsAdIF7xVFFcOz1wrQRQhnhBQC6INh22eVQRoQywgsAdEHbyEtwhJcjNYQXhC7CCwB0gTny8lWQjLwwbYRQRngBgC7oF2QjL+ZqI3bXRSgivABAFxzb82IYhp+rOTn3yEsc4QWhh/ACAF2QlRAtm01qaHbpcGs/SaByugxVHG2SxLQRQhPhBQC6IDI8TOnxLXumBPrUUXldo8zBoaQYwgtCD+EFALqoX1LLMQGBvlzanDJKiI5QhJ1/5hF6+K4GgC4Klo3qzEMZadZFqCK8AEAXBctGdeV1LJNGaCO8AEAXBctGdeyui1BHeAGALkprbdg1w0GgMnfXTWGZNEIU4QUAushcuVMe6OGldYM6Rl4QqggvANBFSTERkqTyuiY/V9K5tmkjh58rAXyD8AIAXZTYOvJSVd8kpytwd9k1l0qz2gihivACAF2U2DryYhhS5dHAHX3hUEaEOsILAHRRhD1M8VHhktoCQiBitRFCHeEFADxgNu1W1AVmeDEMw91QzGojhCrCCwB4INCbdquONqu5tR+HkReEKsILAHggqTUQlAfoyEtZ6zLpOEe4HOF2P1cD+AbhBQA8EOh7vZi9OEmxEX6uBPAdwgsAeCAxwKeN2OMFVkB4AQAPBHrDLnu8wAoILwDggUDveWGPF1gB4QUAPOBebVQboNNGNYy8IPQRXgDAA+6G3YAdeeFQRoQ+wgsAeCB4GnYJLwhdhBcA8IAZCirqGmUYgXc4ozkixO66CGWEFwDwgDlt1OwyVNPQ7OdqTnSkhqXSCH2EFwDwQFSEXVERLf90BlrTrmEY7mkjGnYRyggvAOChQG3arWt0qqHZJYmeF4Q2wgsAeCgxQMOLuceLIzxMMZGca4TQRXgBAA8lt54bVBFgK46OnTKy2Wx+rgbwHcILAHjIHHk5EmCHM7r3eGGlEUIc4QUAPGTushto5xuVsdIIFkF4AQAPtTXsBta0EYcywioILwDgoUBdbcShjLAKwgsAeCgp1jwiILDCC0cDwCoILwDgIfdS6QDbpI6RF1gF4QUAPGROGwVcwy7hBRZBeAEADyUHbMNuy1JpGnYR6ggvAOChxNael6NNTtU3Of1cTZu2QxkJLwhthBcA8FC8I1zhYS072AZK0259k1O1jS1BKoV9XhDiCC8A4CGbzabE1o3qAqVp12zWDQ+zqU90uJ+rAXyL8AIA3ZAYYE27ZnhJ4lwjWADhBQC6wWzaPRJg4YVmXVgB4QUAusE9bRQgK47Y4wVWQngBgG5w7/USICdLs8cLrITwAgDdkBgbaCMv7PEC6yC8AEA3JAfY4Yxt00Ysk0bo82l4ue+++zR69GjFxMQoMTGxS88xDEPz589Xdna2oqOjVVhYqG3btvmyTADwWKCdLF1mblAXx8gLQp9Pw0tjY6OmTp2q6667rsvPeeCBB/Twww/r8ccf1/r165WZmamLLrpI1dXVPqwUADwTqA27TBvBCnwaXu6++27dfPPNys/P79LjDcPQo48+qjvuuEM//OEPlZeXp+eee051dXV68cUXfVkqAHgkKTYw93mhYRdWEFA9L3v37lVJSYnGjRvnvs/hcOjCCy/UJ5980uFzGhoaVFVV1e4GAL7mnjYKsNVGjLzACgIqvJSUlEiSMjIy2t2fkZHh/tzxFi5cqISEBPctJyfH53UCQFLrtFFVfbOanS6/1tLkdKnyaMv0FSMvsAKPw8v8+fNls9k6vW3YsKFHRR2/tbVhGN+43fVtt92myspK923//v09ujYAdEVCdIT7zxVH/dv3YjYN22xtxxYAoczj07vmzJmjK664otPHDBgwoFvFZGZmSmoZgcnKynLfX1paesJojMnhcMjhYGkggN4Vbg9Tn6hwVdU3q6KuUalx/vt3yOx3SYyOkD2Mc40Q+jwOL6mpqUpNTfVFLcrNzVVmZqZWrFih4cOHS2pZsbRq1Srdf//9PrkmAHRXcmykquqb/b7i6EgNzbqwFp/2vBQVFWnz5s0qKiqS0+nU5s2btXnzZtXU1LgfM3ToUC1btkxSy3TR3LlztWDBAi1btkyfffaZZs6cqZiYGF155ZW+LBUAPGZO0Rzxc9NuW7Muo9CwBo9HXjxx55136rnnnnN/bI6mfPjhhyosLJQk7dy5U5WVle7H/OpXv9LRo0d1/fXXq7y8XKNGjdLy5csVHx/vy1IBwGNm066/l0uzTBpW49PwsmTJEi1ZsqTTxxiG0e5jm82m+fPna/78+b4rDAC8oG2XXf9OG7kPZWR3XVhEQC2VBoBgkhggRwRwKCOshvACAN2UbJ4s7eeel/Ja9niBtRBeAKCbEgNm2qhl5IXwAqsgvABAN5k9L4HSsMtqI1gF4QUAuikpQE6WZrURrIbwAgDdZJ4s7c+eF5fLcIenFFYbwSIILwDQTe5po6NNJ2z70FsqjzbJ6TLa1QOEOsILAHRTYuu0kdNlqKq+2S81mHu8xEeFKzKcf9JhDXynA0A3RUXYFR1hl+S/pt22Zl1GXWAdhBcA6AGzSdZf5xsdYZk0LIjwAgA9kOg+38g/K47cRwOwTBoWQngBgB5I8vMRAUdqmDaC9RBeAKAHEv2818uR1tCURHiBhRBeAKAHzF4TfzXsmtNV5oZ5gBUQXgCgB8zzjfzVsGtOV7HHC6yE8AIAPZDk54Zd87qJjLzAQggvANAD/m7YNaerEhl5gYUQXgCgB/zdsFtxlJ4XWA/hBQB6INmPhzM6XYYqW8NLAuEFFkJ4AYAe8Oe0UdXRJpnnQSZGM20E6yC8AEAPmNNGDc0uHW109uq1zSmjOAeHMsJa+G4HgB6Ic4QrPMwmqfdHX8zrJUQzZQRrIbwAQA/YbDb37ra9vddLhXt3XcILrIXwAgA95K+9Xtp216XfBdZCeAGAHkr0U9OuuTybaSNYDeEFAHqobeSld8NLJUcDwKIILwDQQ8nunpfenTYq52gAWBThBQB6yH/TRhwNAGsivABAD/lt2oijAWBRhBcA6KG2kZfenjYyR14IL7AWwgsA9FCyn6aNKtw9L0wbwVoILwDQQ+Ymcf4KL6w2gtUQXgCgh8yRj4peXG3U2OxSTUNzy/XZ5wUWQ3gBgB4yRz6qG5rV5HT1yjXNZl2bTepDeIHFEF4AoIcSoiNkazmbsdeOCDBXNvWJipC99WBIwCoILwDQQ/Ywm3uL/t7qeymvY5k0rIvwAgBeYE4dlffSydIVbFAHCyO8AIAXmHut9NZeLxUcDQALI7wAgBeYIy+9tctuxVEOZYR1EV4AwAvMEHGkl3teGHmBFRFeAMAL2s436t3VRonRjLzAeggvAOAFSbG93bDbutoolpEXWA/hBQC8oLcbds0l2QlsUAcLIrwAgBf09uGMnGsEKyO8AIAXJBJegF5DeAEALzB7T3qrYbfcvUkd00awHsILAHjBsfu8uFyGT69V3+RUQ3PLAZCEF1gR4QUAvMAMES5Dqqr37eiLOeoSHmZTnCPcp9cCAhHhBQC8wBFuV2ykXZLvVxwdezSAzcaJ0rAewgsAeElvNe2WcygjLI7wAgBe0ta069vw4h55YY8XWBThBQC8xH2+UW1vTRsx8gJrIrwAgJf01snS5rRREiuNYFGEFwDwkiT3EQG+njZijxdYG+EFALykrWGXaSPAlwgvAOAl7pEXH58sXX7MUmnAiggvAOAlSbG9s1S68qjZ88LIC6yJ8AIAXtLWsOvrHXYZeYG1EV4AwEuSemmTOnfDbjQjL7AmwgsAeEmie7VRkwzDN4czGobhHtkxN8UDrIbwAgBektza89LY7FJdo9Mn16hpaFZz66nV9LzAqggvAOAlMZF2Rdpb/ln11dSROeriCA9TVITdJ9cAAh3hBQC8xGazuaeOfNW0654yYtQFFkZ4AQAv8nXTbjm76wKEFwDwJjNUHPHRRnUVR1kmDRBeAMCLzKZd300bsUEdQHgBAC9K9PW0US0jLwDhBQC8KMnXDbtHzZ4XRl5gXYQXAPAiczrHZz0v7tVGjLzAuggvAOBFvj6ckaMBAB+Hl/vuu0+jR49WTEyMEhMTu/ScmTNnymaztbudd955viwTALzG19NGHMoI+Di8NDY2aurUqbruuus8et6ECRNUXFzsvr399ts+qhAAvMvXDbvukRd6XmBh4b588bvvvluStGTJEo+e53A4lJmZ6YOKAMC3UlqnjcpqGmUYhmw2m1df39znhZ4XWFlA9rysXLlS6enpGjx4sGbNmqXS0tJvfGxDQ4Oqqqra3QDAX9LiHZKko01O1Xr5cEany1Cle5M6Rl5gXQEXXi6++GItXbpUH3zwgRYtWqT169frO9/5jhoaGjp8/MKFC5WQkOC+5eTk9HLFANAm1hGu2MiWAxNLq+q9+trV9U0yWg6UVkI0Iy+wLo/Dy/z5809oqD3+tmHDhm4XdPnll+v73/++8vLyNGnSJL3zzjvatWuX3nrrrQ4ff9ttt6mystJ9279/f7evDQDekN4nSpJUWt3xL13dZTbrxjnCFRkecL97Ar3G456XOXPm6Iorruj0MQMGDOhuPSfIyspS//799cUXX3T4eYfDIYfD4bXrAUBPpcU5tPdwrQ/CC4cyAlI3wktqaqpSU1N9UUuHysrKtH//fmVlZfXaNQGgJ9L6tPxCdcjL4aWSZdKAJB/3vBQVFWnz5s0qKiqS0+nU5s2btXnzZtXU1LgfM3ToUC1btkySVFNTo1tuuUVr1qzRvn37tHLlSk2aNEmpqam69NJLfVkqAHhNemvTbmm1d3teyjmUEZDk46XSd955p5577jn3x8OHD5ckffjhhyosLJQk7dy5U5WVlZIku92urVu36vnnn1dFRYWysrI0duxY/fWvf1V8fLwvSwUAr0mPb+l5OVTlm54XmnVhdT4NL0uWLDnpHi+G2TovKTo6Wu+9954vSwIAn2sbefH2tBEjL4AUgEulASDYpfls2ogN6gCJ8AIAXpfuo4Zdc3fdBEZeYHGEFwDwMrPnpbyuSY3NLq+9boV72oiRF1gb4QUAvCwxOkIR9pYzjQ7VeG/0hdVGQAvCCwB4WViYTalxrX0vXjwioMJcbcTICyyO8AIAPmCuOPJm30uFu2GXkRdYG+EFAHwgLd675xs1OV2qaWiW1DItBVgZ4QUAfMBcceSt8GKOuthsUh/CCyyO8AIAPtA2beSdnhdzpVFCdITsYTavvCYQrAgvAOAD7o3qvHREgLnHC1NGAOEFAHzCfb6Rl5ZKl9e2jLwk0qwLEF4AwBfSvT3y0trzksgyaYDwAgC+YDbsHq5pkMtlnOTRJ1dxlA3qABPhBQB8ICW2Jbw0uwwdaW227YlyRl4AN8ILAPhAZHiYkmNbRkm8sVGde9oompEXgPACAD7i7nvxSnhpnTaKZeQFILwAgI+0LZfu+V4v5qGMrDYCCC8A4DPpXjwioG3aiJEXgPACAD6S5sXDGTmUEWhDeAEAH/HmydLmUmlWGwGEFwDwmbbDGXvW81Lf5FR9k0sS4QWQCC8A4DPe6nkxm3XDw2yKc4T3uC4g2BFeAMBHjj2c0TC6v8vusUcD2GycKA0QXgDAR8yel6NNTtU2Orv9OiyTBtojvACAj8Q6whUbaZfUs71e2lYa0e8CSIQXAPCp9D4973sxw0sCRwMAkggvAOBTaV44IsCcNmLkBWhBeAEAH/LGEQGVRzlRGjgW4QUAfMi9UV1ND0ZeamnYBY5FeAEAHzL3ejlU1ZNpI44GAI5FeAEAH0r3Qs9LJUcDAO0QXgDAh9oadrvf81JeR88LcCzCCwD4kHm+UU8OZ+REaaA9wgsA+JDZ81Je16TGZpfHzzcMQxV1TBsBxyK8AIAPJcVEKMLech5Rd1Yc1TQ0q9lltL4WIy+ARHgBAJ+y2WxKi+v+Xi/mlJEjPExREXav1gYEK8ILAPhYT3bZpd8FOBHhBQB8LM3c66Ub4aWcfhfgBIQXAPAxc8VRt0ZeOBoAOAHhBQB8zH1EQDf2eqlwH8rItBFgIrwAgI+1Hc7Y/Z4XzjUC2hBeAMDH3OcbdWOpND0vwIkILwDgY+leGHlJIrwAboQXAPAxs2H3cE2DXK0bznWVe3fdaKaNABPhBQB8LLV1k7pml6EjrWGkqziUETgR4QUAfCzCHqbk2JaRE0+njipbl0onxTLyApgILwDQC9zLpT1s2nU37EYz8gKYCC8A0Avalkt3fa8Xp8twj7ywVBpoQ3gBgF5gLpf2ZJfd6vomGa39vQmMvABu4f4uwF+cTqeampr8XQZCTEREhOx2Tv7FidLcu+x2PbyYzbpxjnBFhvO7JmCyXHgxDEMlJSWqqKjwdykIUYmJicrMzJTNZvN3KQgg6d0KL2xQB3TEcuHFDC7p6emKiYnhBwy8xjAM1dXVqbS0VJKUlZXl54oQSNoOZ+x6z0sly6SBDlkqvDidTndwSUlJ8Xc5CEHR0dGSpNLSUqWnpzOFBLfu9LyUcygj0CFLTaKaPS4xMTF+rgShzPz+oqcKxzr2iADD6NouuxzKCHTMUuHFxFQRfInvL3TEbNg92uRUTUNzl55TwR4vQIcsGV4AoLfFOsIVG9kyjdjVpt1yDmUEOkR4sbh9+/bJZrNp8+bN/i4FCHnpfTzre6lo3aAugWkjoB3CC/xq5syZmjJlir/LAHqFe5fdro681JoNu4y8AMcivASpxkbPTqYNNE6nUy6Xy99lAL0q3YMjAuqbnPq0qFySNCg9zqd1AcGG8BIkCgsLNWfOHM2bN0+pqam66KKLJEnbt2/XxIkTFRcXp4yMDE2bNk2HDx92P+/dd9/VBRdcoMTERKWkpOiSSy7Rnj17PLr2gAEDdO+99+rKK69UXFycsrOz9dhjj7V7zMMPP6z8/HzFxsYqJydH119/vWpqatyfX7JkiRITE/Xmm2/q9NNPl8Ph0NVXX63nnntOr7/+umw2m2w2m1auXNn9NwkIcGkeHM740a5Dqmt0qm9itPL7Jvi6NCCoWD68GIahusZmv9y6ulzS9Nxzzyk8PFyrV6/W008/reLiYl144YU666yztGHDBr377rv6+uuvddlll7mfU1tbq3nz5mn9+vV6//33FRYWpksvvdTjUY8HH3xQZ5xxhj799FPddtttuvnmm7VixQr358PCwvTHP/5Rn332mZ577jl98MEH+tWvftXuNerq6rRw4UL9+c9/1rZt2/THP/5Rl112mSZMmKDi4mIVFxdr9OjRHtUFBBNzr5dDVScPL+9+ViJJGv8tdmsGjmepTeo6crTJqdPvfM8v195+z3jFRHb9f8GgQYP0wAMPuD++8847dfbZZ2vBggXu+/7nf/5HOTk52rVrlwYPHqwf/ehH7V7jL3/5i9LT07V9+3bl5eV1+drnn3++fv3rX0uSBg8erNWrV+uRRx5xjwDNnTvX/djc3Fzde++9uu666/TEE0+4729qatITTzyhM888031fdHS0GhoalJmZ2eVagGCV3sWel8Zml1bs+FqSdHE+fzeA41l+5CWYjBw5st3HGzdu1Icffqi4uDj3bejQoZLknhras2ePrrzySp166qnq06ePcnNzJUlFRUUeXbugoOCEj3fs2OH++MMPP9RFF12kvn37Kj4+XtOnT1dZWZlqa2vdj4mMjNQZZ5zh0XWBUNLVIwI+2XNY1fXNSot3aMQpSb1RGhBULD/yEh1h1/Z7xvvt2p6IjY1t97HL5dKkSZN0//33n/BY81ydSZMmKScnR88++6yys7PlcrmUl5fnlYZfcyj7P//5jyZOnKjZs2fr3nvvVXJysv75z3/q2muvbbfLbHR0NMPfsLSurjZqmzLKUFgYf2eA41k+vNhsNo+mbgLJ2Wefrddee00DBgxQePiJX0NZWZl27Nihp59+WmPGjJEk/fOf/+zWtdauXXvCx+Yoz4YNG9Tc3KxFixYpLKxlMO+VV17p0utGRkbK6XR2qyYg2Jg9LxV1TWpodsoRfuIvMM1Ol97b1hJeLs7jcE+gI0wbBbEbbrhBR44c0U9+8hOtW7dOX375pZYvX65rrrlGTqdTSUlJSklJ0TPPPKPdu3frgw8+0Lx587p1rdWrV+uBBx7Qrl279Kc//UmvvvqqbrrpJknSwIED1dzcrMcee0xffvmlXnjhBT311FNdet0BAwZoy5Yt2rlzpw4fPsx5QAhpSTERirC3jKQcrul49HPd3iMqr2tSUkyERuUm92Z5QNAgvASx7OxsrV69Wk6nU+PHj1deXp5uuukmJSQkKCwsTGFhYXr55Ze1ceNG5eXl6eabb9aDDz7YrWv993//tzZu3Kjhw4fr3nvv1aJFizR+fMt021lnnaWHH35Y999/v/Ly8rR06VItXLiwS687a9YsDRkyRCNHjlRaWppWr17drfqAYGCz2ZQW1/leL++0ThmNOz1T4Xb+iQY6YjM8Xa8b4KqqqpSQkKDKykr16dOn3efq6+u1d+9e5ebmKioqyk8VBp8BAwZo7ty57VYU4ZvxfYbOTP7Tav17f4WenjZC47/VfiWRy2XovIXvq7S6QYuvPkdjh6T7qUqg93X28/t4xHoA6EXmyEtHhzN+WlSu0uoGxUeF6/yBqb1dGhA0CC8A0IvalkufGF7MKaPvDctQZDj/PAPfxGd/O/bt26drr71Wubm5io6O1sCBA3XXXXeddImuYRiaP3++srOzFR0drcLCQm3bts1XZaIL9u3bx5QR4CXmRnWHjtvrxTAM9xLpCXlsTAd0xmfh5fPPP5fL5dLTTz+tbdu26ZFHHtFTTz2l22+/vdPnPfDAA3r44Yf1+OOPa/369crMzNRFF12k6upqX5UKAL3GXC5detwRAVsPVOpAxVHFRNp14eA0f5QGBA2fbXAyYcIETZgwwf3xqaeeqp07d+rJJ5/UQw891OFzDMPQo48+qjvuuEM//OEPJbWc55ORkaEXX3xRv/jFL3xVLgD0im/aqM6cMho7JF1RHm5gCVhNr06qVlZWKjn5m/ct2Lt3r0pKSjRu3Dj3fQ6HQxdeeKE++eSTDp/T0NCgqqqqdjcACFRt00Zt4cUwDL2ztVgSU0ZAV/RaeNmzZ48ee+wxzZ49+xsfU1LS8ptHRkZGu/szMjLcnzvewoULlZCQ4L7l5OR4r2gA8DKzYfdwTYNcrpadKj4vqda+sjo5wsM0dijLo4GT8Ti8zJ8/XzabrdPbhg0b2j3n4MGDmjBhgqZOnaqf/exnJ73G8effGIbxjWfi3HbbbaqsrHTf9u/f7+mXBAC9JjXOIZtNanYZOlLXsoDBnDL69uA0xTmC87gSoDd5/Ldkzpw5uuKKKzp9zIABA9x/PnjwoMaOHauCggI988wznT4vM7NluLSkpMR9sKAklZaWnjAaY3I4HHI4HF2sHgD8K8IepuSYSJXVNqq0qkGpcQ69+1nLlNHFTBkBXeJxeElNTVVqatc2Tzpw4IDGjh2rESNGaPHixe5D+75Jbm6uMjMztWLFCg0fPlyS1NjYqFWrVnV4crKVFBYW6qyzztKjjz7q71LYcRfoobR4h8pqG3WopkF7DtVo19c1irDb9N1hHf+SBqA9n41PHjx4UIWFhTrllFP00EMP6dChQ+7PmSMskjR06FAtXLhQl156qWw2m+bOnasFCxbotNNO02mnnaYFCxYoJiZGV155pa9KDQp/+9vfFBER4e8yJEnr169XbGysv8vwC5vNpmXLlmnKlCn+LgVBLC3eoc9LqlVaVa/PDlRKkkYPTFVCdGD8HQcCnc/Cy/Lly7V7927t3r1b/fr1a/e5Y49T2rlzpyorK90f/+pXv9LRo0d1/fXXq7y8XKNGjdLy5csVHx/vq1KDQmertHpbWprv96BobGxUZGSkz6/TVYFWD4Kbe6+X6ga9w5QR4DGfrTaaOXOmDMPo8HYswzA0c+ZM98c2m03z589XcXGx6uvrtWrVKuXl5fmqzKBRWFjYbppmwIAB+t3vfqfp06crLi5O/fv31+uvv65Dhw5p8uTJiouLU35+frvm6bKyMv3kJz9Rv379FBMTo/z8fL300kvtrlNdXa2rrrpKsbGxysrK0iOPPNLhtY+dvrLZbPrzn/+sSy+9VDExMTrttNP0xhtvuD/vdDrb7bY8ZMgQ/eEPf2h33ZkzZ2rKlClauHChsrOzNXjwYN1zzz3Kz88/4b0YMWKE7rzzzg7fp5UrV8pms+mtt97SmWeeqaioKI0aNUpbt2716H0oLCzUnDlzNG/ePKWmpuqiiy5y93KZo4TH9nYBnjBXHG0qKtdnB6oUZpMuOp0pI6CrODzDMKTGWv/cenig9yOPPKLzzz9fmzZt0ve//31NmzZN06dP109/+lN9+umnGjRokKZPn+4OjPX19RoxYoTefPNNffbZZ/r5z3+uadOm6V//+pf7NefNm6fVq1frjTfe0IoVK/Txxx/r008/PWktd999ty677DJt2bJFEydO1FVXXaUjR45Iklwul/r166dXXnlF27dv15133qnbb79dr7zySrvXeP/997Vjxw6tWLFCb775pq655hpt375d69evdz9my5Yt2rRpU7vA25Ff/vKXeuihh7R+/Xqlp6frBz/4gZqamrr8PkgtGySGh4dr9erVevrpp911LF68WMXFxe3qAjxhHs74/uelkqRRuSlKiWPhAdBVrMlrqpMWZPvn2rcflCK73zsyceJE967Dd955p5588kmdc845mjp1qiTp1ltvVUFBgb7++mtlZmaqb9++uuWWW9zPv/HGG/Xuu+/q1Vdf1ahRo1RdXa3nnntOL774or773e9KavlBnZ198vdn5syZ+slPfiJJWrBggR577DGtW7dOEyZMUEREhO6++273Y3Nzc/XJJ5/olVde0WWXXea+PzY2Vn/+85/bTc+MHz9eixcv1jnnnOOu58ILL9Spp57aaT133XWXLrroIkktIaRfv35atmyZLrvsspO+D6ZBgwbpgQceOOG1ExMT2/VtAZ4yR17M318m5vP9BHiCkZcgdsYZZ7j/bC4lP3aaxbyvtLTltzun06n77rtPZ5xxhlJSUhQXF6fly5erqKhIkvTll1+qqalJ5557rvs1EhISNGTIEI9qiY2NVXx8vPu6kvTUU09p5MiRSktLU1xcnJ599ln3dU35+fkn9JXMmjVLL730kurr69XU1KSlS5fqmmuuOWk9BQUF7j8nJydryJAh2rFjR5feB9PIkSNPeh2gO8yeF0my2aTx3yK8AJ5g5CUipmUExF/X7snTj1l9ZG7i19F9LpdLkrRo0SI98sgjevTRR5Wfn6/Y2FjNnTvXfdK3Ob3U0SaBntRivoZ53VdeeUU333yzFi1apIKCAsXHx+vBBx88YZqmoxVMkyZNksPh0LJly+RwONTQ0KAf/ehHJ62nI+bXdbL3obN6AG8wjwiQpBGnJCm9T1QnjwZwPMKLzdajqZtg8vHHH2vy5Mn66U9/Kqkl1HzxxRcaNmyYJGngwIGKiIjQunXr3McsVFVV6YsvvtCFF17Yo+uOHj1a119/vfu+PXv2dOm54eHhmjFjhhYvXiyHw6ErrrhCMTEnD31r167VKaecIkkqLy/Xrl27NHToUHc9nb0PnYmIiJDT6exS7cA3STsmvHCWEeA5wouFDBo0SK+99po++eQTJSUl6eGHH1ZJSYn7h3Z8fLxmzJihX/7yl0pOTlZ6erruuusuhYWFfePxDF297vPPP6/33ntPubm5euGFF7R+/Xrl5uZ26fk/+9nP3DWuXr26S8+55557lJKSooyMDN1xxx1KTU11781ysvehMwMGDND777+v888/Xw6HQ0lJSV2qBzhWrCNc/VNi9HVVvS7Ozzr5EwC0Q8+Lhfz2t7/V2WefrfHjx6uwsFCZmZknbLb28MMPq6CgQJdccom+973v6fzzz9ewYcMUFdX9Ye3Zs2frhz/8oS6//HKNGjVKZWVl7UZhTua0007T6NGjNWTIkHYNtZ35/e9/r5tuukkjRoxQcXGx3njjDXc/TVfeh2+yaNEirVixQjk5Oe5doIHueGnWeXrzxjHqmxjt71KAoGMzutLQEESqqqqUkJCgyspK9enTp93n6uvrtXfvXuXm5vboh7GV1NbWqm/fvlq0aJGuvfZav9RgGIaGDh2qX/ziF5o3b16nj125cqXGjh2r8vJyJSYm9k6Bx+H7DAA819nP7+MxbYR2Nm3apM8//1znnnuuKisrdc8990iSJk+e7Jd6SktL9cILL+jAgQO6+uqr/VIDACCwEF5wgoceekg7d+5UZGSkRowYoY8//rjLh3F6W0ZGhlJTU/XMM8/QXwIAkER4wXGGDx+ujRs3+rsMN09nNQsLCz1+DgAguNCwCwAAgoolwwu/mcOX+P4CAN+yVHgxd4Gtq6vzcyUIZeb31/G7DgMAvMNSPS92u12JiYnuM3diYmJ6tPkacCzDMFRXV6fS0lIlJibKbrf7uyQACEmWCi+S3KcBH3toIOBNnDoNAL5lufBis9mUlZWl9PR0NTU1+bschJiIiAhGXADAxywXXkx2u50fMgAABCFLNewCAIDgR3gBAABBhfACAACCSsj1vJgbhFVVVfm5EgAA0FXmz+2ubPQZcuGlurpakpSTk+PnSgAAgKeqq6uVkJDQ6WNsRojtZe5yuXTw4EHFx8f3eAO6qqoq5eTkaP/+/erTp4+XKgxtvGee4f3yDO+X53jPPMP75TlvvWeGYai6ulrZ2dkKC+u8qyXkRl7CwsLUr18/r75mnz59+Cb2EO+ZZ3i/PMP75TneM8/wfnnOG+/ZyUZcTDTsAgCAoEJ4AQAAQYXw0gmHw6G77rpLDofD36UEDd4zz/B+eYb3y3O8Z57h/fKcP96zkGvYBQAAoY2RFwAAEFQILwAAIKgQXgAAQFAhvAAAgKBCeOmiH/zgBzrllFMUFRWlrKwsTZs2TQcPHvR3WQFr3759uvbaa5Wbm6vo6GgNHDhQd911lxobG/1dWsC67777NHr0aMXExCgxMdHf5QSkJ554Qrm5uYqKitKIESP08ccf+7ukgPXRRx9p0qRJys7Ols1m09///nd/lxTQFi5cqHPOOUfx8fFKT0/XlClTtHPnTn+XFbCefPJJnXHGGe6N6QoKCvTOO+/02vUJL100duxYvfLKK9q5c6dee+017dmzRz/+8Y/9XVbA+vzzz+VyufT0009r27ZteuSRR/TUU0/p9ttv93dpAauxsVFTp07Vdddd5+9SAtJf//pXzZ07V3fccYc2bdqkMWPG6OKLL1ZRUZG/SwtItbW1OvPMM/X444/7u5SgsGrVKt1www1au3atVqxYoebmZo0bN061tbX+Li0g9evXT7///e+1YcMGbdiwQd/5znc0efJkbdu2rVeuz1LpbnrjjTc0ZcoUNTQ0KCIiwt/lBIUHH3xQTz75pL788kt/lxLQlixZorlz56qiosLfpQSUUaNG6eyzz9aTTz7pvm/YsGGaMmWKFi5c6MfKAp/NZtOyZcs0ZcoUf5cSNA4dOqT09HStWrVK3/72t/1dTlBITk7Wgw8+qGuvvdbn12LkpRuOHDmipUuXavTo0QQXD1RWVio5OdnfZSAINTY2auPGjRo3bly7+8eNG6dPPvnET1UhlFVWVkoS/2Z1gdPp1Msvv6za2loVFBT0yjUJLx649dZbFRsbq5SUFBUVFen111/3d0lBY8+ePXrsscc0e/Zsf5eCIHT48GE5nU5lZGS0uz8jI0MlJSV+qgqhyjAMzZs3TxdccIHy8vL8XU7A2rp1q+Li4uRwODR79mwtW7ZMp59+eq9c29LhZf78+bLZbJ3eNmzY4H78L3/5S23atEnLly+X3W7X9OnTZbVZN0/fM0k6ePCgJkyYoKlTp+pnP/uZnyr3j+68X/hmNput3ceGYZxwH9BTc+bM0ZYtW/TSSy/5u5SANmTIEG3evFlr167VddddpxkzZmj79u29cu3wXrlKgJozZ46uuOKKTh8zYMAA959TU1OVmpqqwYMHa9iwYcrJydHatWt7bZgsEHj6nh08eFBjx45VQUGBnnnmGR9XF3g8fb/QsdTUVNnt9hNGWUpLS08YjQF64sYbb9Qbb7yhjz76SP369fN3OQEtMjJSgwYNkiSNHDlS69ev1x/+8Ac9/fTTPr+2pcOLGUa6wxxxaWho8GZJAc+T9+zAgQMaO3asRowYocWLFysszHoDfT35HkObyMhIjRgxQitWrNCll17qvn/FihWaPHmyHytDqDAMQzfeeKOWLVumlStXKjc3198lBR3DMHrtZ6Klw0tXrVu3TuvWrdMFF1ygpKQkffnll7rzzjs1cOBAS426eOLgwYMqLCzUKaecooceekiHDh1yfy4zM9OPlQWuoqIiHTlyREVFRXI6ndq8ebMkadCgQYqLi/NvcQFg3rx5mjZtmkaOHOkeySsqKqKP6hvU1NRo9+7d7o/37t2rzZs3Kzk5WaeccoofKwtMN9xwg1588UW9/vrrio+Pd4/yJSQkKDo62s/VBZ7bb79dF198sXJyclRdXa2XX35ZK1eu1Lvvvts7BRg4qS1bthhjx441kpOTDYfDYQwYMMCYPXu28dVXX/m7tIC1ePFiQ1KHN3RsxowZHb5fH374ob9LCxh/+tOfjP79+xuRkZHG2WefbaxatcrfJQWsDz/8sMPvpxkzZvi7tID0Tf9eLV682N+lBaRrrrnG/XcxLS3N+O53v2ssX768167PPi8AACCoWK8JAQAABDXCCwAACCqEFwAAEFQILwAAIKgQXgAAQFAhvAAAgKBCeAEAAEGF8AIAAIIK4QUAAIv66KOPNGnSJGVnZ8tms+nvf/+7z6954MAB/fSnP1VKSopiYmJ01llnaePGjR69BuEFAACLqq2t1ZlnnqnHH3+8V65XXl6u888/XxEREXrnnXe0fft2LVq0SImJiR69DscDAAAA2Ww2LVu2TFOmTHHf19jYqN/85jdaunSpKioqlJeXp/vvv1+FhYXdusavf/1rrV69Wh9//HGPamXkBQAAdOjqq6/W6tWr9fLLL2vLli2aOnWqJkyYoC+++KJbr/fGG29o5MiRmjp1qtLT0zV8+HA9++yzHr8OIy8AAOCEkZc9e/botNNO01dffaXs7Gz34773ve/p3HPP1YIFCzy+RlRUlCRp3rx5mjp1qtatW6e5c+fq6aef1vTp07v8OuEeXxkAAIS8Tz/9VIZhaPDgwe3ub2hoUEpKiiRp3759ys3N7fR1brjhBndPjcvl0siRI93BZ/jw4dq2bZuefPJJwgsAAOgZl8slu92ujRs3ym63t/tcXFycJKlv377asWNHp6+TlJTk/nNWVpZOP/30dp8fNmyYXnvtNY9qI7wAAIATDB8+XE6nU6WlpRozZkyHj4mIiNDQoUO7/Jrnn3++du7c2e6+Xbt2qX///h7VRngBAMCiampqtHv3bvfHe/fu1ebNm5WcnKzBgwfrqquu0vTp07Vo0SINHz5chw8f1gcffKD8/HxNnDjR4+vdfPPNGj16tBYsWKDLLrtM69at0zPPPKNnnnnGo9ehYRcAAItauXKlxo4de8L9M2bM0JIlS9TU1KTf/e53ev7553XgwAGlpKSooKBAd999t/Lz87t1zTfffFO33XabvvjiC+Xm5mrevHmaNWuWR69BeAEAAEGFfV4AAEBQIbwAAICgQngBAABBhfACAACCCuEFAAAEFcILAAAIKoQXAAAQVAgvAAAgqBBeAABAUCG8AACAoEJ4AQAAQeX/Ay2HLbdZQN11AAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x,GS_left[:,int(len(y)/2),int(len(z)/2)].real, label=\"real part\")\n",
    "plt.plot(x,GS_left[:,int(len(y)/2),int(len(z)/2)].imag, label=\"imaginary part\")\n",
    "#plt.plot(x,pot[:,int(len(y)/2),int(len(z)/2)], label=\"potential (rescaled)\")\n",
    "plt.legend()\n",
    "plt.show()\n",
    "\n",
    "plt.plot(x,GS_right[:,int(len(y)/2),int(len(z)/2)].real, label=\"real part\")\n",
    "plt.plot(x,GS_right[:,int(len(y)/2),int(len(z)/2)].imag, label=\"imaginary part\")\n",
    "#plt.plot(x,pot[:,int(len(y)/2),int(len(z)/2)], label=\"potential (rescaled)\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1333.33x500 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#state_plot = GS_left.real\n",
    "#state_plot = GS_left.imag\n",
    "state_plot1 = np.abs(GS_left)**2\n",
    "\n",
    "state_plot2 = np.abs(GS_right)**2\n",
    "\n",
    "# Create a 1xn_states grid of subplots (1 row, n_states columns)\n",
    "fig, ax = plt.subplots(1, 2, figsize=(10/6*n_states, 5))  # Adjust the size as needed\n",
    "\n",
    "# Slice through the y-direction and rotate the x-z plane (by swapping x and z)\n",
    "im = ax[0].imshow(state_plot1[ :, int(len(y)/2), :].T,\n",
    "                extent=[*extend[0], *extend[2]], origin=\"lower\",\n",
    "                vmin=np.min(state_plot1), vmax=np.max(state_plot1))\n",
    "\n",
    "# Set labels\n",
    "ax[0].set_xlabel(\"x\")\n",
    "ax[0].set_ylabel(\"z\")\n",
    "ax[0].set_title(f\"left\")\n",
    "fig.colorbar(im, ax=ax[0])\n",
    "\n",
    "im = ax[1].imshow(state_plot2[ :, int(len(y)/2), :].T,\n",
    "                extent=[*extend[0], *extend[2]], origin=\"lower\",\n",
    "                vmin=np.min(state_plot2), vmax=np.max(state_plot2))\n",
    "\n",
    "# Set labels\n",
    "ax[1].set_xlabel(\"x\")\n",
    "ax[1].set_ylabel(\"z\")\n",
    "ax[1].set_title(f\"right\")\n",
    "fig.colorbar(im, ax=ax[1])  \n",
    "\n",
    "# Adjust layout for better spacing\n",
    "plt.tight_layout()\n",
    "\n",
    "# Show the plots\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Calculate results:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_J(state_left, state_right, hamiltonian, dvol):\n",
    "    \"\"\"\n",
    "    Calculates the single-particle hopping amplitude between\n",
    "    the two input states, which normally should be lowest energy states of\n",
    "    the two wells.\n",
    "    \"\"\"\n",
    "    #flatten the wavefunctions for calculation\n",
    "    state_left_flat = state_left.reshape((-1,))\n",
    "    state_right_flat = state_right.reshape((-1,))\n",
    "\n",
    "    #calculate J\n",
    "    integrand  = -state_left_flat.conj() * (hamiltonian @ state_right_flat)\n",
    "\n",
    "    return np.sum(integrand)*np.prod(dvol)\n",
    "\n",
    "def get_U_s(state,mass,scatter_length, dvol):\n",
    "    \"\"\"\n",
    "    Calculates onsite interaction due to contact interaction\n",
    "    \"\"\"\n",
    "    #integrate psi**4\n",
    "    integrand = np.abs(state)**4\n",
    "    total_integral = np.sum(integrand)*np.prod(dvol)\n",
    "\n",
    "    print(total_integral)\n",
    "    #add factor and return\n",
    "    return 4*np.pi*const.hbar*scatter_length/mass * total_integral\n",
    "\n",
    "def get_U_dd(state, mu, pol, dvol):\n",
    "    \"\"\"Calculates the onsite interaction due to dipolar interactions\n",
    "        :pol (3,) array giving the direction of polarisation\n",
    "    \"\"\"\n",
    "    \n",
    "    raise Exception(\"not yet implemented!\")\n",
    "    x3D, y3D, z3D = np.meshgrid(x,y,z,indexing=\"ij\")\n",
    "    x3D_, y3D_, z3D_ = np.meshgrid(x,y,z,indexing=\"ij\")\n",
    "\n",
    "    location_vectors = np.vstack([x3D.flatten(), y3D.flatten(), z3D.flatten()]).T\n",
    "    location_vectors_ = np.vstack([x3D.flatten(), y3D.flatten(), z3D.flatten()]).T\n",
    "\n",
    "    integral = 0\n",
    "    for i, r in enumerate(location_vectors):\n",
    "        for j, r_ in enumerate(location_vectors_):\n",
    "            cos_theta = ((r[0]*r_[0] + r[1]*r_[1] + r[2]*r_[2])/(r[0]**2 + r[1]**2 + r[2]**2)/(r_[0]**2 + r_[1]**2 + r_[2]**2))\n",
    "            #integral += state[]\n",
    "\n",
    "    \"\"\"\n",
    "    def integrand(x,y,z, x_,y_,z_):\n",
    "        cos_theta = (x*x_ + y*y_ + z*z_)/((x**2 + y**2 + z**2)*(x_**2 + y_**2 + z_**2))\"\"\"\n",
    "    \n",
    "\n",
    "def get_U(state_left, state_right, hamiltonian, mass, scatter_length, mu):\n",
    "    \"\"\"Calculates the total onsite interaction\"\"\"\n",
    "    U_s = get_U_s(state_left, state_right, hamiltonian)\n",
    "    #U should be different if tweezers are not identical, use left one here\n",
    "    U_dd = get_U_dd(state_left,...)\n",
    "    return U_s + U_dd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "J = -0.18035688997810906Hz    imaginary part: 0.0Hz\n"
     ]
    }
   ],
   "source": [
    "J_Hz = get_J(GS_left, GS_right, ham, dvol) / const.h\n",
    "print(f\"J = {J_Hz.real}Hz    imaginary part: {J_Hz.imag}Hz\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---------"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.615142490815278e+18\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "1.4049588450401188e+35"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a0 = const.physical_constants[\"Bohr radius\"][0]\n",
    "\n",
    "get_U_s(GS_left, float(trap.subs(trap.m)), 100*a0, dvol)/const.h"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x,np.abs(GS_left[:,int(len(y)/2),int(len(z)/2)])**2, label=\"square\")\n",
    "#plt.plot(x,np.abs(GS_left[:,int(len(y)/2),int(len(z)/2)])**4, label=\"power 4\")\n",
    "#plt.plot(x,pot[:,int(len(y)/2),int(len(z)/2)], label=\"potential (rescaled)\")\n",
    "plt.legend()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "base",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}